diff --git "a/AdE0T4oBgHgl3EQfxgLI/content/tmp_files/load_file.txt" "b/AdE0T4oBgHgl3EQfxgLI/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/AdE0T4oBgHgl3EQfxgLI/content/tmp_files/load_file.txt" @@ -0,0 +1,1944 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf,len=1943 +page_content='Climate change heterogeneity: A new quantitative approach ∗ Mar´ıa Dolores Gadea Rivas † University of Zaragoza Jes´us Gonzalo ‡ U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Carlos III de Madrid July 10, 2022 Abstract Climate change is a non-uniform phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This paper proposes a new quantitative methodology to characterize, measure and test the existence of climate change heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' It consists of three steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' First, we introduce a new testable warming typology based on the evolution of the trend of the whole temperature distribution and not only on the average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Second, we define the concepts of warming acceleration and warming amplification in a testable for- mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' And third, we introduce the new testable concept of warming dominance to determine whether region A is suffering a worse warming process than region B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Applying this three-step methodology, we find that Spain and the Globe ex- perience a clear distributional warming process (beyond the standard average) but of different types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In both cases, this process is accelerating over time and asymmetrically amplified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Overall, warming in Spain dominates the Globe in all the quantiles except the lower tail of the global temperature distribution that corresponds to the Artic region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Our climate change heterogeneity results open the door to the need for a non-uniform causal-effect climate analysis that goes beyond the standard causality in mean as well as for a more efficient design of the mitigation-adaptation policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In particular, the heterogeneity we find suggests that these policies should contain a common global component and a clear local-regional element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Future climate agreements should take the whole temperature distribution into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' JEL classification: C31, C32, Q54 Keywords: Climate change;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate heterogeneity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Global-Local Warming;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Functional stochastic processes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Distributional characteristics;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Trends;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Quan- tiles;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Temperature distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' ∗The authors gratefully acknowledge the financial support from the Gobierno de Aragon and FEDER funds (grant, LMP71-18), the Spanish Ministerio de Ciencia y Tecnolog´ıa, Agencia Espa˜nola de Investi- gaci´on (AEI) and European Regional Development Fund (ERDF, EU) under grants PID2019-104960GB- IOO, ECO2017-83255-C3-1-P (AEI/ERDF, EU) and ECO2016-81901-REDT, and Bank of Spain (ER grant program).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' We thank Rodrigo Gonzalez Laiz for excellent research assistance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' † Department of Applied Economics, University of Zaragoza.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Gran V´ıa, 4, 50005 Zaragoza (Spain).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Tel: +34 9767 61842, fax: +34 976 761840 and e-mail: lgadea@unizar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='es ‡ Department of Economics, University Carlos III, Madrid 126 28903 Getafe (Spain).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Tel: +34 91 6249853, fax: +34 91 6249329 and e-mail: jesus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='gonzalo@uc3m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='es (corresponding author) 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='02648v1 [econ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='EM] 6 Jan 2023 Climate change heterogeneity 2 1 Introduction All the assessment reports (AR) published by the Intergovernmental Panel of Cli- mate Change (IPCC) show that there is overwhelming scientific evidence of the existence of global warming (GW).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' It is also well known that climate change (CC) is a non-uniform phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' What is not so clear is the degree of heterogeneity across all the regions in our planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In fact, an important part of the Sixth Assess- ment Report (AR6) published by the IPCC in 2021-2022 is dedicated to this issue: climate (warming) heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This is reflected in the chapters studying regional climate change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Our paper introduces a new quantitative methodology that builds on that described in Gadea and Gonzalo 2020 (GG2020) to characterize, measure and test the existence of such climate change heterogeneity (CCH).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This is done in three steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' First, we introduce a warming typology (W1, W2 and W3) based on the trending behavior of the quantiles of the temperature distribution of a given ge- ographical location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Second, we define in a testable format the concepts of warming acceleration and warming amplification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' These concepts help to characterize (more ordinally than cardinally) the warming process of different regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' And third, we propose the new concept of warming dominance (WD) to establish when region A suffers a worse warming process than region B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' We have chosen Spain as a benchmark geographical location because, as the AR6 report states “.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Spain is fully included in the Mediterranean (MED) Reference Region, but is one of the most climatically diverse countries in the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' ”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This fact opens up the possibility of studying warming heterogeneity (WH) from Spain to the Globe (outer heterogeneity, OWH) and also from Spain to some of its regions represented by Madrid and Barcelona (inner heterogeneity, IWH).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The three steps rely on the results reported in GG2020, where the different distributional characteristics (moments, quantiles, inter quantile range, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=') of the temperature distribution of a given geographical location are converted into time series objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' By doing this, we can easily implement and test all the concepts involved in the three steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' A summary of the results is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Spain and the Globe present a clear warming process;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' but it evolves differently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Spain goes from a warming process where lower and upper temperatures share the same trend behavior (IQR is maintained constant over time, warming type W1) to one characterized by a larger increase in the upper temperatures (IQR increases over time, warming type W3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In contrast, Climate change heterogeneity 3 the Globe as a whole maintains a stable warming type process characterized by lower temperatures that increase more than the upper ones (IQR decreases in time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='1 In our typology, this constitutes a case of warming type W2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate heterogeneity can go further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' For instance, within Spain we find that Madrid is of type W3 while the warming process of Barcelona is of type W1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This is in concordance with the Madrid climate being considered a Continental Mediterranean climate while Barcelona is more a pure Mediterranean one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The proposed warming typology (W1, W2 and W3), although dynamic, is more ordinal than cardinal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In this paper, the strength of a warming process is captured in the second step by analyzing its acceleration and its amplification with respect to a central tendency measure of the temperature distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Acceleration and amplification contribute to the analysis of warming heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The acceleration in the Globe is present in all the quantiles above q30 while in Spain it already becomes significant above the 10th quantile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' We find an asymmetric behavior of warming amplification;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' in Spain (in comparison with the Globe mean temperature) this is present in the upper temperatures (above the 80th and 90th quantiles) while in the Globe the opposite occurs (below the 20th and 30th quantiles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Within Spain, Madrid and Barcelona also behave differently in terms of acceleration and amplifi- cation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Overall, warming in Spain dominates that of the Globe in all the quantiles except for the lower quantile q05, and between Madrid and Barcelona there is a par- tial WD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Madrid WD Barcelona in the upper part of the distribution and Barcelona WD Madrid in the lower one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The existence of a clear heterogeneous warming process opens the door to the need of a new non-uniform causal (effect) research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' One that goes beyond the stan- dard causality in mean analysis (see Tol, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' CCH also suggests that in order for the mitigation-adaptation policies to be as efficient as possible they should be designed following a type of common factor structure: a common global compo- nent plus an idiosyncratic local element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This goes in the line with the results found in Brock and Xepapadeas (2017), D’Autume et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (2016) and Peng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Future climate agreements should clearly have this CCH into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' An important by-product of our warming heterogeneity results is the increase that this heterogeneity can generate in the public awareness of the GW process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' A possible explanation for that can be found in the behavioral economics work by Malmendier 1Similar results for Central England are found in GG2020 and for the US in Diebold and Rude- bush, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 4 (2021), in the results of the European Social Survey analyzed in Nowakowski and Oswald (2020) or in the psychology survey by Maiella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The rest of the paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Section 2 describes our basic climate econometrics methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Section 3 presents a brief description of the temperature data from Spain and the Globe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Section 4 addresses the application of our quantita- tive methodology in the cross-sectional version (temperatures measured monthly by stations in an annual interval) to Spain and (versus) the Globe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' It also reports the results of applying the methodology using a purely temporal dimension (local daily temperature on an annual basis) for two representative stations in Spain (Madrid and Barcelona, empirical details in the Appendix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Section 5 offers a comparison and interpretation of the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Finally, Section 6 concludes the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 2 Climate Econometrics Methodology In this section, we briefly summarize the novel econometric methodology introduced in GG2020 to analyze Global and Local Warming processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Following GG2020, Warming is defined as an increasing trend in certain characteristics of the temper- ature distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' More precisely: Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (Warming): Warming is defined as the existence of an increas- ing trend in some of the characteristics measuring the central tendency or position (quantiles) of the temperature distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' An example is a deterministic trend with a polynomial function for certain val- ues of the β parameters Ct = β0 + β1t + β2t2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' + βktk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In GG2020 temperature is viewed as a functional stochastic process X = (Xt(ω), t ∈ T), where T is an interval in R, defined in a probability space (Ω, ℑ, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' A conve- nient example of an infinite-dimensional discrete-time process consists of associating ξ = (ξn, n ∈ R+) with a sequence of random variables whose values are in an appro- priate function space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This may be obtained by setting Xt(n) = ξtN+n, 0 ≤ n ≤ N, t = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T (1) so X = (Xt, t = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' If the sample paths of ξ are continuous, then we have a sequence X0, X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='. of random variables in the space C[0, N].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The choice of the period or segment t will depend on the situation in hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In our case, t will be the Climate change heterogeneity 5 period of a year, and N represents cross-sectional units or higher-frequency time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' We may be interested in modeling the whole sequence of G functions, for instance the sequence of state densities (f1(ω), f2(ω), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', fT (ω) ) as in Chang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (2015, 2016) or only certain characteristics (Ct(w)) of these G functions, for instance, the state mean, the state variance, the state quantile, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' These characteristics can be considered time series objects and, therefore, all the econometric tools already developed in the time series literature can be applied to Ct(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' With this charac- teristic approach we go from Ω to RT , as in a standard stochastic process, passing through a G functional space: Ω (w) X −→ G Xt(w) C−→ R Ct(w) Going back to the convenient example and abusing notation, the stochastic struc- ture can be summarized in the following array: X10(w) = ξ0(w) X11(w) = ξ1(w) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' X1N(w) = ξN(w) C1(w) X20(w) = ξN+1(w) X21(w) = ξN+2(w) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' X2N(w) = ξ2N(w) C2(w) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' XT0(w) = ξ(T−1)N+1(w) XT1(w) = ξ(T−1)N+2(w) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' XTN(w) = ξTN(w) CT (w) (2) The objective of this section is to provide a simple test to detect the existence of a general unknown trend component in a given characteristic Ct of the temperature process Xt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' To do this, we need to convert Definition 1 into a more practical definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (Trend test): Let h(t) be an increasing function of t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' A characteristic Ct of a functional stochastic process Xt contains a trend if β ̸= 0 in the regression Ct = α + βh(t) + ut, t = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (3) The main problem of this definition is that the trend component in Ct as well as the function h(t) are unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Therefore this definition can not be easily imple- mented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' If we assume that Ct does not have a trend component (it is I(0))2 and 2Our definition of an I(0) process follows Johansen (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' A stochastic process Yt that satisfies Yt − E(Yt) = ∞ � i=1 Ψiεt−i is called I(0) if ∞ � i=1 Ψ izi converges for |z| < 1 + δ, for some δ > 0 and ∞ � i=1 Ψ i ̸= 0, where the condition εt ∼ iid(0,σ2) with σ2 > 0 is understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 6 h(t) is linear, then we have the following well known result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Let Ct = I(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the regression Ct = α + βt + ut (4) the OLS estimator �β = T� t=1 (Ct − C)(t − t) T� t=1 (t − t)2 (5) satisfies T 3/2 �β = Op(1) (6) and asymptotically (T → ∞) tβ=0 is N(0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In order to analyze the behavior of the t-statistic tβ = 0, for a general trend component in Ct, it is very convenient to use the concept of Summability (Berenguer- Rico and Gonzalo, 2014) Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (Order of Summability): A trend h(t) is said to be summable of order “δ” (S(δ)) if there exists a slowly varying function L(T),3 such that ST = 1 T 1+δ L(T) T � t=1 h(t) (8) is O(1), but not o(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Let Ct = h(t) + I(0) such that h(t) is S(δ) with δ ≥ 0, and such that the function g(t) = h(t)t is S(δ + 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the regression Ct = α + βt + ut (9) the OLS �β estimator satisfies T (1−δ) �β = Op(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (10) Assuming that the function h(t)2 is S(1 + 2δ − γ) with 0 ≤ γ ≤ 1 + δ, then 3A positive Lebesgue measurable function, L, on (0, ∞) is slowly varying (in Karamata’s sense) at ∞ if L(λn) L(n) → 1 (n → ∞) ∀λ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (7) (See Embrechts et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', 1999, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 564).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 7 tβ=0 = � Op(T γ/2) for 0 ≤ γ ≤ 1 Op(T 1/2) for 1 ≤ γ ≤ 1 + δ (11) Examples of how this proposition applies for different particular Data Generat- ing Processes (DGP) can be found in GG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' A question of great empirical importance is how our trend test (TT) of Proposi- tion 2 behaves when Ct = I(1) (accumulation of an I(0) process).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Following Durlauf and Phillips (1988), T 1/2 �β = Op(1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' however, tβ=0 diverges as T→∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Therefore, our TT can detect the stochastic trend generated by an I(1) process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In fact, our test will detect trends generated by any of the three standard persistent processes considered in the literature (see Muller and Watson, 2008): (i) fractional or long- memory models;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (ii) near-unit-root AR models;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' and (iii) local-level models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Let Ct = µ + zt, t = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (12) In the first model, zt is a fractional process with 1/2 < d < 3/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the second model, zt follows an AR, with its largest root close to unity, ρT = 1 − c/T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the third model, zt is decomposed into an I(1) and an I(0) component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Its simplest format is zt = υt + ϵt with υt = υt−1 +ηt, where ϵt is ID(0, q ∗ σ2), ηt is ID(0, σ2), σ2 > 0 and both disturbances are serially and mutually independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Note that the pure unit-root process is nested in all three models: d = 1, c = 0, and q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The long-run properties implied by each of these models can be characterized using the stochastic properties of the partial sum process for zt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The standard assumptions considered in the macroeconomics or finance literature assume the ex- istence of a “δ,” such that T −1/2+δ �T t=1 zt −→ σ H(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' ), where “δ” is a model-specific constant and H is a model-specific zero-mean Gaussian process with a given covari- ance kernel k(r, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Then, it is clear that the process Ct = µ + zt is summable (see Berenguer-Rico and Gonzalo, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This is the main reason why Proposition 3 holds for these three persistent processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Let Ct = µ + zt, t = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T, with zt any of the following three processes: (i) a fractional or long-memory model, with 1/2 < d < 3/2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (ii) a near- unit-root AR model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' or (iii) a local-level model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Furthermore, T −1/2+δ �T t=1 zt −→ σ H(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' ), where “δ” is a model-specific constant and H is a model-specific zero-mean Gaussian process with a given covariance kernel k(r, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Then, in the LS regression Ct = α + βt + ut, Climate change heterogeneity 8 the t-statistic diverges, tβ=0 = Op(T 1/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' After the development of the theoretical core, we are in a position to design tools to approach the empirical strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The following subsection describes each of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='1 Empirical tools: definitions and tests From Propositions 2 and 3, Definition 2 can be simplified into the following testable and practical definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (Practical definition 2): A characteristic Ct of a functional stochas- tic process Xt contains a trend if in the LS regression, Ct = α + βt + ut, t = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T, (13) β = 0 is rejected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Several remarks are relevant with respect to this definition: (i) regression (13) has to be understood as the linear LS approximation of an unknown trend function h(t) (see White, 1980);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (ii) the parameter β is the plim of �βols;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (iii) if the regression (13) is the true data-generating process, with ut ∼ I(0), then the OLS �β estimator is asymptotically equivalent to the GLS estimator (see Grenander and Rosenblatt, 1957);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (iv) in practice, in order to test β = 0, it is recommended to use a robust HAC version of tβ=0 (see Busetti and Harvey, 2008);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' and (v) this test only detects the existence of a trend but not the type of trend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' For all these reasons, in the empirical applications we implement Definition 4 by estimating regression (13) using OLS and constructing a HAC version of tβ=0 (Newey and West, 1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' These linear trends can be common across characteristics indicating similar pat- ters in the time evolution of these characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (Co-trending): A set of m distributional characteristics (C1t,C2t,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=',Cmt) do linearly co-trend if in the multivariate regression � � C1t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Cmt � � = � � α1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' αm � � + � � β1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' βm � � t + � � u1t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' umt � � (14) Climate change heterogeneity 9 all the slopes are equal, β1 = β2 = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' = βm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 4 This co-trending hypothesis can be tested by a standard Wald test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' When m = 2 an alternative linear co-trending test can be obtained from the regression Cit − Cjt = α + βt + ut i ̸= j i, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', m by testing the null hypothesis of β = 0 vs β ̸= 0 using a simple tβ=0 test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate classification is a tool used to recognize, clarify and simplify the existent climate heterogeneity in the Globe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' It also helps us to better understand the Globe’s climate and therefore to design more efficient global warming mitigation policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The prevalent climate typology is that proposed by K¨oppen (1900) and later on modified in K¨oppen and Geiger (1930).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' It is an empirical classification that divides the climate into five major types, which are represented by the capital letters A (tropical zone), B (dry zone), C (temperate zone), D (continental zone), and E (polar zone).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Each of these climate types except for B is defined by temperature criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' More recent classifications can been found in the AR6 of the IPCC (2021, 2022) but all of them share the spirit of the original one of K¨oppen (1900).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The climate classification we propose in this section is also based on temperature data and it has three simple distinctive characteristics: It considers the whole temperature distribution and not only the average It has a dynamic nature: it is based on the evolution of the trend of the temperature quantiles (lower and upper).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' It can be easily tested Definition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (Warming Typology): We define four types of warming processes: W0: There is no trend in any of the quantiles (No warming).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' W1: All the location distributional characteristics have the same positive trend (dispersion does not contain a trend) W2: The Lower quantiles have a larger positive trend than the Upper quantiles (dispersion has a negative trend) W3: The Upper quantiles have a larger positive trend than the Lower quantiles (dispersion has a positive trend).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 4This definition is slightly different from the one in Carrion-i-Silvestre and Kim (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 10 Climate is understood, unlike weather, as a medium and long-term phenomenon and, therefore, it is crucial to take trends into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Notice that this typology can be used to describe macroclimate as well as microclimate locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Most of the literature on Global or Local warming only considers the trend behavior of the central part of the distribution (mean or median).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' By doing this, we are losing very useful information that can be used to describe the whole warming process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This information is considered in the other elements of the typology W1, W2 and W3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This typology does not say anything about the intensity of the warming process and its dynamic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Part of this intensity is captured in the following definitions of warming acceleration and warming amplification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Definition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (Warming Acceleration): We say that there is warming acceler- ation in a distributional temperature characteristic Ct between the time periods t1 = (1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', s) and t2 = (s + 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T) if in the following two regressions: Ct = α1 + β1t + ut, t = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', s, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T, (15) Ct = α2 + β2t + ut, t = s + 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T, (16) the second trend slope is larger than the first one: β2 > β1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In practice, we implement this definition by testing in the previous system the null hypothesis β2 = β1 against the alternative β2 > β1 An alternative warming acceleration test can be formed by testing for a structural break at t = s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Neverthe- less, we prefer the approach of Definition 7 because it matches closely the existent narrative on warming acceleration in the climate literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Definition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (Warming Amplification with respect to the mean): We say that there is a warming amplification in distributional characteristic Ct with respect the mean if in the following regression: Ct = β0 + β1meant + ϵt (17) the mean slope is greater than one: β1 > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' When the mean, meant, and Ct come from the same distribution, we name this “inner” warming amplification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Otherwise, the mean may come from an external environment and, in that case, we call it “outer” warming amplification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Both concepts, acceleration and amplification, introduce a quantitative dimen- sion to the ordinarily defined classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' For example, the acceleration, which Climate change heterogeneity 11 has a dynamic character, allows us to observe the transition from one type of cli- mate to another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Amplification, on the other hand, makes it possible to compare the magnitude of the trends that define each type of climate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' It should be noted that, although static in nature, it can be computed recursively at different points in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the previous definitions, we classify the warming process of different regions which is crucial in the design of local mitigation and adaptation policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' But we, also, need to compare the different climate change processes of two regions in order to characterize climate heterogeneity independently of the type of warming they are experimenting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' For this purpose, we propose the following definition that shares the spirit of the stochastic dominance concept used in the economic-finance literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Definition 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (Warming Dominance (WD): We say that the temperature distri- butions of Region A warming dominates (WD) the temperature distributions of Region B if in the following regression qτt(A) − qτt(B) = ατ + βτt + uτt, (18) βτ ≥ 0 for all 0 < τ < 1 and there is at least one value τ ∗ for which a strict inequality holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' It is also possible to have only partial (WD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' For instance, in the lower or upper quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 3 The data 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='1 Spain The measurement of meteorological information in Spain started in the eighteenth century.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' However, it was not until the mid-nineteenth century that reliable and reg- ular data became available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In Spain, there are four main sources of meteorological information: the Resumen Anual, Bolet´ın Diario, Bolet´ın Mensual de Climatolog´ıa and Calendario Meteorol´ogico.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' These were first published in 1866, 1893, 1940 and 1943, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' A detailed explanation of the different sources can be found in Carreras and Tafunell (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Currently, AEMET (Agencia Estatal de Meterolog´ıa) is the agency responsible for storing, managing and providing meteorological data to the public.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Some of the historical publications, such as the Bolet´ın Diario and Calendario Meteorol´ogico can Climate change heterogeneity 12 be found in digital format in their respective archives for whose use it is necessary to use some kind of Optical Character Recognition (OCR) software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='5 In 2015, AEMET developed AEMET OpenData, an Application Programming Interface (API REST) that allows the dissemination and reuse of Spanish meteoro- logical and climatological information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' To use it, the user needs to obtain an API key to allow access to the application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Then, either through the GUI or through a programming language such as Java or Python, the user can request data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' More information about the use of the API can be found on their webpage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='6 In this paper, we are concerned with Spanish daily station data, specifically temperature data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Each station records the minimum, maximum and average tem- perature as well as the amount of precipitation, measured as liters per square meter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The data period ranges from 1920 to 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' However, in 1920 there were only 13 provinces (out of 52) who had stations available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' It was not until 1965 that all the 52 provinces had at least one working station.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Moreover, it is important to keep in mind that the number of stations has increased substantially from only 14 stations in 1920 to more than 250 in 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' With this information in mind, we select the longest span of time that guarantees a wide sample of stations so that all the geographical areas of peninsular Spain are represented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' For this reason, we decided to work with station data from 1950 to 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' There are 30 stations whose geographical distri- bution is displayed in the map in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The original daily data are converted into monthly data, so that we finally work with a total of 30x12 station-month units corresponding to peninsular Spain and, consequently, we have 360 observations each year with which to construct the annual distributional characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='2 The Globe In the case of the Globe, we use the database of the Climate Research Unit (CRU) that offers monthly and yearly data of land and sea temperatures in both hemi- spheres from 1850 to the present, collected from different stations around the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='7 Each station temperature is converted to an anomaly, taking 1961-1990 as the base 5http : //www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='aemet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='es/es/conocermas/recursosenlinea/calendarios?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='n = todos and https : //repositorio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='aemet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='es/handle/20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='11765/6290.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 6https : //opendata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='aemet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='es/centrodedescargas/inicio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The use of AEMET data is regulated in the following resolution https : //www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='boe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='es/boe/dias/2016/01/05/pdfs/BOE − A − 2016 − 111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 7We use CRUTEM version 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0, which can be downloaded from (https://crudata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='uea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='uk/cru/data/temperature/).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' A recent revision of the methodology can be found in Jones et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 13 period, and each grid-box value, on a five-degree grid, is the mean of all the station anomalies within that grid box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This database (in particular, the annual temper- ature of the Northern Hemisphere) has become one of the most widely used to illustrate GW from records of thermometer readings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' These records form the blade of the well-known “hockey stick” graph, frequently used by academics and other institutions, such as, the IPCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In this paper, we prefer to base our analysis on raw station data, as in GG2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The database provides data from 1850 to nowadays, although due to the high variability at the beginning of the period it is customary in the literature to begin in 1880.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In this work, we have selected the stations that are permanently present in the period 1950-2019 according to the concept of the station-month unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In this way, the results are comparable with those obtained for Spain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Although there are 10,633 stations on record, the effective number fluctuates each year and there are only 2,192 stations with data for all the years in the sample period, which yields 19,284 station-month units each year (see this geographical distribution in the map in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='8 In summary, we analyze raw global data (stations instead of grids) for the period 1950 to 2019, compute station-month units that remain all the time and with these build the annual distributional characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 4 Empirical strategy In this section we apply our three-step quantitative methodology to show the ex- istent climate heterogeneity between Spain and the Globe as well as within Spain, between Madrid and Barcelona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Because all our definitions are written in a test- ing format, it is straightforward to empirically apply them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' First, we test for the existence of warming by testing the existence of a trend in a given distributional characteristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' How common are the trends of the different characteristics (revealed by a co-trending test) determine the warming typology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Second, the strength of the warming process is tested by testing the hypothesis of warming acceleration and warming amplification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' And third, independently of the warming typology, we determine how the warming process of Spain compares with that of the Globe as a whole (we do the same for Madrid and Barcelona).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This is done by testing for warming dominance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 8In the CRU data there are 115 Spanish stations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' However, after removing stations not present for the whole 1880 to 2019 period, only Madrid-Retiro, Valladolid and Soria remain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Since 1950, applying the same criteria, only 30 remain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 14 (a) Spain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Selected stations, AEMET data 1950-2019 (b) The Globe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Selected stations, CRU data 1950-2019 Figure 1 Geographical distribution of stations The results are presented according to the following steps: first, we apply our trend test (see Definition 4) to determine the existence of local or global warming and test for any possible warming acceleration;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' second, we test different co-trending 45 18d:w 135°W 90 45° S 90Climate change heterogeneity 15 hypotheses to determine the type of warming of each area;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' thirdly, we test the warming amplification hypothesis for different quantiles with respect to the mean (of Spain as well as of the Globe): H0 : β1 = 1 versus Ha : β1 > 1 in (17);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' and finally, we compare the CC of different regions, for Spain and the Globe, and within Spain, between Madrid and Barcelona, with our warming dominance test (see 18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='9 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='1 Local warming: Spain The cross-sectional analysis is approached under two assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' First, choosing a sufficiently long and representative period of the geographical diversity of the Span- ish Iberian Peninsula, 1950-2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Second, we work with month-station units from daily observations to construct the annual observations of the time series object from the data supplied by the stations, following a methodology similar to that carried out for the whole planet in GG2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='10 The study comprises the steps described in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The density of the data and the evolution of characteristics are displayed, respectively in Figures 2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' We find positive and significant trends in the mean, max, min and all the quan- tiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Therefore from definition 1, we conclude there exists a clear local warming (see Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The recursive evolution for the periods 1950-2019 and 1970-2019 shows a clear increase in the trends of the mean, some dispersion measures and higher quantiles (see the last column of Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' More precisely, there is a significant trend acceler- ation in most of the distributional characteristics except the lower quantiles (below q20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' These quantiles, q05 and q10, remain stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The co-trending tests for the full sample 1950-2019 show a similar evolution of the trend for all the quantiles with a constant iqr (see Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This indicates that in this period the warming process of Spain can be considered a W1 type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' More recently, 1970-2019, the co-trending tests (see Table 3) indicate the upper quantiles grow faster than the lower ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This, together with a positive trend in the dispersion measured by the iqr shows that Spain has evolved from a W1 to a 9Before testing for the presence of trends in the distributional characteristics of the data, we test for the existence of unit roots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' To do so, we use the well-known Augmented Dickey-Fuller test (ADF;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Dickey and Fuller, 1979), where the number of lags is selected in accordance with the SBIC criterion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The results, available from the authors on request, show that the null hypothesis of a unit root is rejected for all the characteristics considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 10The results with daily averages are very similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The decision to work with monthly data instead of daily in the cross-sectional approach has been based on its compatibility with the data available for the Globe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 16 W3 warming type process Finally, no evidence of “inner” amplification during the period 1950-2019 is found in the lower quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Regarding the upper quantiles, we found both “inner” and “outer” amplification in the second period, which supports the previous finding of a transition from type W1 to type W3 (see Table 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Summing up, with our proposed tests for the evolution of the trend of the whole temperature distribution, we conclude that Spain has evolved from a W1 type to a much more dangerous W3 type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The results of acceleration and dynamic amplifi- cation reinforce the finding of this transition to type W3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Figure 2 Spain annual temperature density calculated with monthly data across stations 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='03 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='02 - 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='09796 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='17936 1970 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='739249 1960 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='65786 1950 temperature in degrees Celsius (month-station units)2010 2000 1990 1980 vears0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='07Climate change heterogeneity 17 Figure 3 Characteristics of temperature data in Spain with stations selected since 1950 (monthly data across stations, AEMET, 1950-2019) 30 15 mean max 13 25 1950 1970 1990 2010 1950 1970 1990 2010 0 6 min std 1950 1970 1990 2010 1950 1970 1990 2010 35 range 30 iqr 8 25 1950 1970 1990 2010 1950 1970 1990 2010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='5 kurtosis skewness 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='2 1950 1970 1990 2010 1950 1970 1990 2010 20 10 0 1950 1970 1990 2010 q5 q10 q20 q30 q40 q50 q60 q70 q80 q90 q95Climate change heterogeneity 18 Table 1 Trend acceleration hypothesis (Spain monthly data across stations, AEMET, 1950-2019) Trend test by periods Acceleration test names/periods 1950-2019 1970-2019 1950-2019, 1970-2019 mean 0.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0478 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='3143 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0006) q80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0275 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0471 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='6949 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0040) q90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0321 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0548 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='2441 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0007) q95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0335 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0526 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='3568 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0005) Note: OLS estimates and HAC p-values in parenthesis of the tβ=0 test from regression: Ct = α + βt + ut, for two different time periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' For the acceleration hypothesis we run the system: Ct = α1 + β1t + ut, t = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', s, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T, Ct = α2 + β2t + ut, t = s + 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T, and test the null hypothesis β2 = β1 against the alternativeβ2 > β1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' We show the value of the t-statistic and its HAC p-value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Table 2 Co-trending analysis (Spain monthly data across stations, AEMET, 1950-2019) Joint hypothesis tests Wald test p-value All quantiles (q05, q10,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=',q90, q95) 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='235 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='211 Lower quantiles (q05, q10, q20, q30) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='310 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='958 Medium quantiles (q40, q50, q60) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='438 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='803 Upper quantiles (q70, q80, q90, q95) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='515 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='679 Lower-Medium quantiles (q05, q10, q20, q30, q40, q50, q60) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='771 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='993 Medium-Upper quantiles (q40, q50, q60, q70, q80, q90, q95) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='331 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='215 Lower-Upper quantiles (q05, q10, q20,q30, q70, q80, q90, q95 ) 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='705 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='111 Spacing hypothesis Trend-coeff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' p-value q50-q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='786 q95-q50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='012 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 q95-q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='011 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='096 q75-q25 (iqr) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='179 Note: Annual distributional characteristics (quantiles) of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The top panel shows the Wald test of the null hypothesis of equality of trend coefficients for a given set of characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the bottom panel, the TT is applied to the difference between two representative quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 19 Table 3 Co-trending analysis (Spain monthly data across stations, AEMET, 1970-2019) Joint hypothesis tests Wald test p-value All quantiles (q05, q10,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=',q90, q95) 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='879 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 Lower quantiles (q05, q10, q20, q30) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='121 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='373 Medium quantiles (q40, q50, q60) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='314 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='518 Upper quantiles (q70, q80, q90, q95) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='719 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='633 Lower-Medium quantiles (q05, q10, q20, q30, q40, q50, q60) 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='771 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='047 Medium-Upper quantiles (q40, q50, q60, q70, q80, q90, q95) 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='675 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='099 Lower-Upper quantiles (q05, q10, q20,q30, q70, q80, q90, q95 ) 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='892 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 Spacing hypothesis Trend-coeff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' p-value q50-q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='020 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='029 q95-q50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='012 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='050 q55-q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='032 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='002 q75-q25 (iqr) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='016 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='003 Note: Annual distributional characteristics (quantiles) of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The top panel shows the Wald test of the null hypothesis of equality of trend coefficients for a given set of characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the bottom panel, the TT is applied to the difference between two representative quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Table 4 Amplification hypothesis (Spain monthly data, AEMET 1950-2019 periods/variables 1950-2019 1970-2019 1950-2019 1970-2019 Inner Outer q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='80 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='191) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='051) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='008) Note: OLS estimates and HAC p-values of the t-statistic of testing H0 : βi = 1 versus Ha : βi > 1 in the regression: Cit = βi0 + βi1meant + ϵit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' mean refers to the average of the Spanish Global temperature distribution for the “inner” and “outer”cases, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 20 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='2 Global warming: the Globe In this section, we carry out a similar analysis to that described in the previous subsection for Spain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Figures 4 and 5 show the time evolution of the Global temper- ature densities and their different distributional characteristics from 1950 to 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The data in both figures are obtained from stations that report data throughout the sample period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Table 5 shows a positive trend in the mean as well as in all the quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This indicates the clear existence of Global warming, more pronounced (larger trend) in the lower part of the distribution (a negative trend in the dispersion measures).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The warming process suffers an acceleration in all the quantiles above q30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' From the co-trending analysis (see Tables 6 and 7) we can determine the type of warming process characterizing the whole Globe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Table 6 indicates that in the period 1950-2019 the Globe experimented a W2 warming type (the lower part of the temperature distribution grows faster than the middle and upper part, implying iqr and std have a negative trend).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Similar results are maintained for the period 1970-2019 (in this case only the dispersion measure std has a negative trend).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The asymmetric amplification results shown in Table 8 reinforce the W2 typology for the whole Globe: an increase of one degree in the global mean temperature increases the lower quantiles by more than one degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This does not occur with the upper part of the distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Notice that this amplification goes beyond the standard Artic amplification (q05) affecting also q10, q20 and q30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Summing up, the results from our different proposed tests for the evolution of the trend of the whole temperature distribution indicate that the Globe can be cataloged as a undergoing type W2 warming process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This warming type may have more serious consequences for ice melting, sea level increases, permafrost, CO2 migration, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' than the other types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 21 Figure 4 Global annual temperature density calculated with monthly data across stations 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='025 density 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='015 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='01 - 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='6962 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='5404 1970 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='3846 1960 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='2288 1950 temperature in degrees Celsius (month-station units)2010 2000 1990 1980 vears0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='035Climate change heterogeneity 22 Figure 5 Characteristics of temperature data in the 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0410) Note: OLS estimates and HAC p-values in parenthesis of the tβ=0 test from regression: Ct = α + βt + ut, for two different time periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' For the acceleration hypothesis we run the system: Ct = α1 + β1t + ut, t = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', s, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T, Ct = α2 + β2t + ut, t = s + 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T, and test the null hypothesis β2 = β1 against the alternativeβ2 > β1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' We show the value of the t-statistic and its HAC p-value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Table 6 Co-trending analysis (CRU montly data, 1950-2019) Joint hypothesis tests Wald test p-value All quantiles (q05, q10,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=',q90, q95) 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='005 Lower quantiles (q05, q10, q20, q30) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='545 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='023 Medium quantiles (q40, q50, q60) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='078 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='962 Upper quantiles (q70, q80, q90, q95) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='099 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='777 Lower-Medium quantiles (q05, q10, q20, q30, q40, q50, q60) 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='691 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='007 Medium-Upper quantiles (q40, q50, q60, q70, q80, q90, q95) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='041 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='916 Lower-Upper quantiles (q05, q10, q20,q30, q70, q80, q90, q95 ) 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='683 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='001 Spacing hypothesis Trend-coeff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' p-value q50-q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='022 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 q95-q50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='004 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='193 q95-q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='026 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 q75-q25 (iqr) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='007 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='043 Note: Annual distributional characteristics (quantiles) of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The top panel shows the Wald test of the null hypothesis of equality of trend coefficients for a given set of characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the bottom panel, the TT is applied to the difference between two representative quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 24 Table 7 Co-trending analysis (CRU montly data, 1970-2019) Joint hypothesis tests Wald test p-value All quantiles (q05, q10,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=',q90, q95) 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='478 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='047 Lower quantiles (q05, q10, q20, q30) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='523 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='137 Medium quantiles (q40, q50, q60) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='569 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='752 Upper quantiles (q70, q80, q90, q95) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='667 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='446 Lower-Medium quantiles (q05, q10, q20, q30, q40, q50, q60) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='606 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='268 Medium-Upper quantiles (q40, q50, q60, q70, q80, q90, q95) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='714 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='348 Lower-Upper quantiles (q05, q10, q20,q30, q70, q80, q90, q95 ) 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='520 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='043 Spacing hypothesis Trend-coeff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' p-value q50-q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='020 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='047 q95-q50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='003 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='462 q95-q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='023 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='048 q75-q25 (iqr) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='004 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='418 Note: Annual distributional characteristics (quantiles) of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The top panel shows the Wald test of the null hypothesis of equality of trend coefficients for a given set of characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the bottom panel, the TT is applied to the difference between two representative quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Table 8 Amplification hypotheses (CRU monthly data across stations, 1950-2019) periods/variables 1950-2019 1970-2019 q05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='83 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000) q10 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='79 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='73 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='001) q20 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='41 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='37 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000) q30 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='07 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='00 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='089) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='502) q40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='88 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='91 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='999) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='973) q50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='74 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='81 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} 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+page_content='69 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='70 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000) (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000) q95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='64 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000) (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000) Note: OLS estimates and HAC p-values of the t-statistic of testing H0 : βi = 1 versus Ha : βi > 1 in the regression: Cit = βi0 +βi1meant +ϵit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' mean refers to the average of the Global temperature distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 25 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='3 Micro-local warming: Madrid and Barcelona The existence of warming heterogeneity implies that in order to design more ef- ficient mitigation policies, they have to be developed at different levels: global, country, region etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' How local we need to go will depend on the existing degree of micro-warming heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In this subsection, we go to the smallest level, cli- mate station level .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' We analyze, within Spain, the warming process in two weather stations corresponding to two cities: Madrid (Retiro station) and Barcelona (Fabra station).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 11 Obviously, the data provided by these stations is not cross-sectional data but directly pure time series data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Our methodology can be easily applied to higher frequency time series, in this case daily data, to compute the distributional characteristics (see Figures A1 and A2)12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The results are shown in the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' These two stations, Madrid-Retiro and Barcelona-Fabra clearly experience two different types of warming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' First, there is evidence of micro-local warming, understood as the presence of significant and positive trends, in all the important temperature distributional characteristics of both stations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The acceleration phenomenon is also clearly detected, in other words, the warming increases as time passes (see Tables A1 and A5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Secondly, from the co-trending tests (Tables A2-A3 and A6-A7), it can be concluded that the warming process of Madrid-Retiro is type W3 while for Barcelona-Fabra it is type W1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In both cases the warming typology is stable through both sample periods (1950-2019 and 1970-2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Thirdly, as expected, Madrid-Retiro presents “inner” and “outer” amplification for the upper quantiles, while Barcelona-Fabra does so only for the center part of its temperature distribution (see Tables A4 and A8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Summing up, even within Spain we find evidence of warming heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' While Madrid (Continental Mediterranean climate) has a similar pattern as that of peninsular Spain (1970-2019) W3, Barcelona (Mediterranean coastline climate) maintains a W1 typology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Thus there are two different warming processes which require mitigation policies at the country as well as the very local level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 11From Madrid and Barcelona there is data since 1920’s, nevertheless we began the study in 1950 for consistency with the previous analysis of Spain and the Globe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 12See the application to Central England in GG2020 and in Gadea and Gonzalo (2022) to Madrid, Zaragoza and Oxford.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 26 5 Comparing results The goal of this section is to show the existence of climate heterogeneity by com- paring the results obtained from applying our three-step methodology to different regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' These results are summarized in Table 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' It is clear that there is distribu- tional warming in all the analyzed areas;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' but this warming follows different patterns and sometimes the warming type is not even stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the case of Spain, it depends on the period under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Figure 6 captures graphically the different trend behavior and intensity of the distributional characteristics by regions (Spain and the Globe and Madrid and Barcelona).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='13 The graphical results in this figure coincide with the results of the warming typology tests shown in Table 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The middle of Table 10 shows that warming acceleration is detected in all the locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This acceleration is more general in Spain than in the Globe (see also the heatmap in Figure 7) and in Barcelona than in Madrid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Apart from these differences, the acceleration shares certain similarities across regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This is not the case for the warming amplification that is clearly asymmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Spain suffers an amplification in the upper quantiles while the Globe does so in the lower ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Notice that the latter amplification goes beyond the standard results found in the literature for the Arctic region (q05).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' We detect amplification also for the regions corresponding to the quantiles q10-q30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the case of Madrid and Barcelona, Madrid suffers a wider warming amplification than Barcelona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The results of the first two steps of our methodology are obtained region by region (Spain, the Globe, Madrid and Barcelona).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' It is the last step, via the warming dominance test (see the numerical results in Table 9) where we compare directly one region with another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Warming in Spain dominates that of the Globe in all the quantiles except the lower q05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='14 This would support the idea held in European institutions and gathered in international reports on the greater intensity of climate 13The analysis of other characteristics such as the third and fourth order moments can contribute to the temperature distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the case of Spain, the kurtosis is always negative with a mean value of -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='8 and a significant negative trend, which means that we are dealing with a platykurtic distribution with tails less thick than Normal, a shape that is accelerating over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' However, it is ot possible to draw conclusions about symmetry given its high variability over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Conversely, the temperature distribution in the Globe is clearly leptokurtic with an average kurtosis of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='9 and a negative but not significant trend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The global temperature observations are therefore more concentrated around the mean and their tails are thicker than in a Normal distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The skewness is clearly negative although a decreasing and significant trend points to a reduction of the negative skewness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 14A more detailed analysis of the warming process suffered in the Artic region can be found in Gadea and Gonzalo (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 27 change in the Iberian Peninsula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Warming in Madrid dominates that of Barcelona in the upper quantiles, while the reverse is the case in the lower quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This latter result coincides with the idea that regions close to the sea have milder upper temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Further research (beyond the scope of this paper) will go in the direction of finding the possible causes behind the warming types W1, W2, and W3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Following the literature, on diurnal temperature asymmetry (Diurnal Temperature Range = DTR = Tmax − Tmin) we can suggest as possible causes for W2 the cloud coverage (Karl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 1993) and the planetary boundary layer (see Davy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' For W3, the process of desertification (see Karl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' 1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Summarizing, in this section we describe, measure and test the existence of warming heterogeneity in different regions of the planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' It is important to note that these extensive results can not be obtained by the standard analysis of the average temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Table 9 Warming dominance Spain-Globe Madrid-Barcelona Quantile β t-ratio β t-ratio q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='018 (-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='770) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='013 (-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='730) q10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='010 (-1.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='019 (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='930) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='014 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='993) Note: The slopes (t-statistic) of the following regression qτt(A) − qτt(B) = ατ + βτt + uτt In the first column A=Spain, B=Globe and in the second A=Madrid, B=Barcelona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 28 Table 10 Summary of results Cross analysis Sample Period Type Acceleration Amplification Dominance Inner Outer Spain 1950-2019 W1 [mean, std, iqr, rank, [q70, q80, q95] [q90, q95] [q60,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q95] q20,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q95] 1970-2019 W3 [q50,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q80] [q60,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q95] The Globe 1950-2019 W2 [mean [q05,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q30] [q05] q40,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q95] 1970-2019 W2 [q05,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q20] Time analysis Sample Period Type Acceleration Amplification Dominance Madrid, Retiro Station 1950-2019 W3 [mean, std, rank, [q50,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q95] [ q40,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q95] [q80,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q95] q40, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q95] 1970-2019 W3 [q50,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q95] [q40,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q95] Barcelona, Fabra Station 1950-2019 W1 [mean, [q30,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q90] [q05,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q40] q20,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q95] 1970-2019 W1 [q60, q70] [q30,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', q70] Note: For Spain and the Globe we build characteristics from station-months units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' For Madrid and Barcelona we use daily frequency time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' A significance level of 10% is considered for all tests and characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 29 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='01 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='06 mean max min std iqr rank kur skw q5 q10 q20 q30 q40 q50 q60 q70 q80 q90 q95 Globe-montly-1950 Spain-montly-1950 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='01 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='06 mean max min std iqr rank kur skw q5 q10 q20 q30 q40 q50 q60 q70 q80 q90 q95 Spain-montly-1950 Madrid-daily-1950 Barcelona-daily-1950 Note: The bars represent the intensity of the trends found in each characteristic measured through the value of the β-coefficient estimated in the regression Ct = α + βt + ut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Figure 6 Trend evolution of different temperature distributional characteristics Climate change heterogeneity 30 1950-2019 1955-2019 1960-2019 1965-2019 1970-2019 1975-2019 1980-2019 1985-2019 1990-2019 1995-2019 2000-2019 mean max min std iqr rank kur skw q5 q10 q20 q30 q40 q50 q60 q70 q80 q90 q95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='02 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='1 (a) Globe Spain 1950-2019 1955-2019 1960-2019 1965-2019 1970-2019 1975-2019 1980-2019 1985-2019 1990-2019 1995-2019 2000-2019 mean max min std iqr rank kur skw q5 q10 q20 q30 q40 q50 q60 q70 q80 q90 q95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='02 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='1 (b) Spain Note: The color scale on the right side of the figure shows the intensity of the trend, based on the value of the β-coefficient estimated in the regression Ct = α + βt + ut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Figure 7 Comparing heatmaps Climate change heterogeneity 31 6 Conclusions The existence of Global Warming is very well documented in all the scientific reports published by the IPCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the last one, the AR6 report (2022), special attention is dedicated to climate change heterogeneity (regional climate).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Our paper presents a new quantitative methodology, based on the evolution of the trend of the whole tem- perature distribution and not only on the average, to characterize, to measure and to test the existence of such warming heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' It is found that the local warm- ing experienced by Spain (one of most climatically diverse areas) is very different from that of the Globe as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In Spain, the upper-temperature quantiles tend to increase more than the lower ones, while in the Globe just the opposite occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In both cases the warming process is accelerating over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Both regions suffer an amplification effect of an asymmetric nature: there is warming amplification in the lower quantiles of the Globe temperature (beyond the standard well-known results of the Arctic zone) and in the upper ones of Spain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Overall, warming in Spain domi- nates that of the Globe in all the quantiles except the lower q05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' This places Spain in a very difficult warming situation compared to the Globe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Such a situation requires stronger mitigation-adaptation policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' For this reason, future climate agreements should take into consideration the whole temperature distribution and not only the average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Any time a novel methodology is proposed, new research issues emerge for future investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Among those which have been left out of this paper (some are part of our current research agenda), three points stand out as important: There is a clear need for a new non-uniform causal-effect climate change anal- ysis beyond the standard causality in mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In order to improve efficiency, mitigation-adaptation policies should be de- signed containing a common global component and an idiosyncratic regional element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The relation between warming heterogeneity and public awareness of climate change deserves to be analyzed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 32 References [1] Berenguer-Rico, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', Gonzalo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Summability of stochastic processes- A generalization of integration and co-integration valid for non-linear processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Journal of Econometrics 178, 331-341.' metadata={'source': 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C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Hsiao and A Timmermann (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' ), Essays in Honor of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Hashem Pesaran (Advances in Econometrics, Volume 43), 9-28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Online appendix here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Code here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Working paper at arXiv:1907.' 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='1 Madrid-Retiro Figure A1 Characteristics of temperature data in Madrid-Retiro (AEMET daily data, 1950-2019) 16 32 30 mean 28 max 1950 1970 1990 2010 2019 1950 1970 1990 2010 2019 5 8 wmw min std 5 6 1950 1970 1990 2010 2019 1950 1970 1990 2010 2019 15 35 rank w 30 10 igr 25 1950 1970 1990 2010 2019 1950 1970 1990 2010 2019 kur 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='5 0 1950 1970 1990 2010 2019 1950 1970 1990 2010 2019 30 20 10 0 1950 1970 1990 2010 2019 q5 q10 q20 q30 q40 q50 q60 q70 q80 q90 q95Climate change heterogeneity 37 Table A1 Trend acceleration hypothesis (Madrid, daily data, AEMET, 1950-2019) Trend test by periods Acceleration test names/periods 1950-2019 1970-2019 1950-2019, 1970-2019 mean 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0326 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0447 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0972 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0687 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='7956 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0374) q95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0527 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0710 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='7839 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0383) Note: OLS estimates and HAC p-values in parenthesis of the tβ=0 test from regression: Ct = α + βt + ut, for two different time periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' For the acceleration hypothesis we run the system: Ct = α1 + β1t + ut, t = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', s, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T, Ct = α2 + β2t + ut, t = s + 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T, and test the null hypothesis β2 = β1 against the alternativeβ2 > β1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' We show the value of the t-statistic and its HAC p-value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Table A2 Co-trending analysis (Madrid-Retiro daily data, AEMET 1950-2019) Joint hypothesis tests Wald test p-value All quantiles (q05, q10,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=',q90, q95) 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='046 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 Lower quantiles (q05, q10, q20, q30) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='360 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='715 Medium quantiles (q40, q50, q60) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='036 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='361 Upper quantiles (q70, q80, q90, q95) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='944 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='268 Lower-Medium quantiles (q05, q10, q20, q30, q40, q50, q60) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='707 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='349 Medium-Upper quantiles (q40, q50, q60, q70, q80, q90, q95) 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='822 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 Lower-Upper quantiles (q05, q10, q20,q30, q70, q80, q90, q95 ) 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='967 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 Spacing hypothesis Trend-coeff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' p-value q50-q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='505 q95-q50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='023 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 q05-q95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='028 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 q75-q25 (iqr) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='027 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 Note: Annual distributional characteristics (quantiles) of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The top panel shows the Wald test of the null hypothesis of equality of trend coefficients for a given set of characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the bottom panel, the TT is applied to the difference between two representative quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 38 Table A3 Co-trending analysis (Madrid-Retiro daily data, AEMET, 1970-2019) Joint hypothesis tests Wald test p-value All quantiles (q05, q10,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=',q90, q95) 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='371 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 Lower quantiles (q05, q10, q20, q30) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='424 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='935 Medium quantiles (q40, q50, q60) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='111 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='017 Upper quantiles (q70, q80, q90, q95) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='214 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='360 Lower-Medium quantiles (q05, q10, q20, q30, q40, q50, q60) 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='687 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 Medium-Upper quantiles (q40, q50, q60, q70, q80, q90, q95) 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='851 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='004 Lower-Upper quantiles (q05, q10, q20,q30, q70, q80, q90, q95 ) 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='094 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 Spacing hypothesis Trend-coeff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' p-value q50-q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='036 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='004 q95-q50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='017 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='051 q05-q95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='053 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 q75-q25 (iqr) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='040 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000 Note: Annual distributional characteristics (quantiles) of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The top panel shows the Wald test of the null hypothesis of equality of trend coefficients for a given set of characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the bottom panel, the TT is applied to the difference between two representative quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Table A4 Amplification hypothesis (Madrid daily data, AEMET 1950-2019) periods/variables 1950-2019 1970-2019 1950-2019 1970-2019 Inner Outer q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='66 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='43 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='83 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='56 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='993) (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='000) (0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='39 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='021) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='007) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='073) Note: OLS estimates and HAC p-values of the t-statistic of testing H0 : βi = 1 versus Ha : βi > 1 in the regression: Cit = βi0 + βi1meant + ϵit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' mean refers to the average of the Madrid or Spanish temperature distribution for the “inner” and “outer”cases, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 39 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='2 Barcelona-Fabra Figure A2 Characteristics of temperature data in Barcelona-Fabra (AEMET daily data, 1950-2019) 16 30 15 14 mean 25 1950 1970 1990 2010 2019 1950 1970 1990 2010 2019 8 5 std www min 5 1950 1970 1990 2010 2019 1950 1970 1990 2010 2019 30 25 igr 20 1950 1970 1990 2010 2019 1950 1970 1990 2010 2019 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='5 kur 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='4 skw 0.' 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0190) q95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0390 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0525 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='3435 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='0907) Note: OLS estimates and HAC p-values in parenthesis of the tβ=0 test from regression: Ct = α + βt + ut, for two different time periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' For the acceleration hypothesis we run the system: Ct = α1 + β1t + ut, t = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', s, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T, Ct = α2 + β2t + ut, t = s + 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=', T, and test the null hypothesis β2 = β1 against the alternativeβ2 > β1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' We show the value of the t-statistic and its HAC p-value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Table A6 Co-trending analysis (Barcelona-Fabra daily data, AEMET, 1950-2019) Joint hypothesis tests Wald test p-value All quantiles (q05, q10,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=',q90, q95) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='368 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='971 Lower quantiles (q05, q10, q20, q30) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='036 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='792 Medium quantiles (q40, q50, q60) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='073 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='964 Upper quantiles (q70, q80, q90, q95) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='784 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='853 Lower-Medium quantiles (q05, q10, q20, q30, q40, q50, q60) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='171 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='978 Medium-Upper quantiles (q40, q50, q60, q70, q80, q90, q95) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='901 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='929 Lower-Upper quantiles (q05, q10, q20,q30, q70, q80, q90, q95 ) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='969 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='888 Spacing hypothesis Trend-coeff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' p-value q50-q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='528 q95-q50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='006 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='233 q05-q95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='856 q75-q25 (iqr) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='004 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='442 Note: Annual distributional characteristics (quantiles) of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The top panel shows the Wald test of the null hypothesis of equality of trend coefficients for a given set of characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the bottom panel, the TT is applied to the difference between two representative quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Climate change heterogeneity 41 Table A7 Co-trending analysis (Barcelona-Fabra daily data, AEMET, 1970-2019) Joint hypothesis tests Wald test p-value All quantiles (q05, q10,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=',q90, q95) 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='165 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='215 Lower quantiles (q05, q10, q20, q30) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='904 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='593 Medium quantiles (q40, q50, q60) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='267 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='531 Upper quantiles (q70, q80, q90, q95) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='384 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='943 Lower-Medium quantiles (q05, q10, q20, q30, q40, q50, q60) 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='103 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='120 Medium-Upper quantiles (q40, q50, q60, q70, q80, q90, q95) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='642 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='949 Lower-Upper quantiles (q05, q10, q20,q30, q70, q80, q90, q95 ) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='693 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='207 Spacing hypothesis Trend-coeff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' p-value q50-q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='019 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='192 q95-q50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='821 q05-q95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='017 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='241 q75-q25 (iqr) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='011 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='189 Note: Annual distributional characteristics (quantiles) of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' The top panel shows the Wald test of the null hypothesis of equality of trend coefficients for a given set of characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' In the bottom panel, the TT is applied to the difference between two representative quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' Table A8 Amplification hypothesis (Barcelona daily data, AEMET 1950-2019) periods/variables 1950-2019 1970-2019 1950-2019 1970-2019 Inner Outer q05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='99 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='432) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='192) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content='298) Note: OLS estimates and HAC p-values of the t-statistic of testing H0 : βi = 1 versus Ha : βi > 1 in the regression: Cit = βi0 + βi1meant + ϵit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'} +page_content=' mean refers to the average of the Barcelona or Spanish temperature distribution for the “inner” and “outer”cases, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AdE0T4oBgHgl3EQfxgLI/content/2301.02648v1.pdf'}