stevevaius/best-monthly-forecast-2026

🏆 Best Monthly Time Series Forecast (2026 SOTA) — v2: Optimized Hybrid Ensemble

v2 Update: Added optimized neural+statistical hybrid ensemble, scipy-optimized weights, per-model comparison across 16 methods. 14% improvement over zero-shot neural baselines.

🔑 Key Finding: When AutoARIMA Beats Neural Models

If your AutoARIMA achieves ~1% sMAPE but neural models give 5-8%, your data has strong, clean monthly seasonality. Here's how to get the best of both worlds:

What Works (Ranked by M4-Monthly sMAPE)

Rank	Method	sMAPE ↓	MASE ↓	Key Insight
🥇	Optimized Ensemble	9.52	0.668	Scipy-optimized weights: 75% TiRex + 11% Chronos-2 + 5% AutoARIMA
🥈	TiRex (zero-shot)	9.65	0.680	Best single model — xLSTM captures periodicity better than transformers
🥉	Top-3 Statistical Ensemble	9.76	0.673	OptTheta + AutoTheta + AutoARIMA average
4	Inv-sMAPE Weighted Ensemble	9.93	0.670	Automatic weight learning from error
5	AutoTheta (s=12)	10.33	0.700	Best single statistical model
6	OptimizedTheta (s=12)	10.63	0.705
7	Chronos-2 (zero-shot)	11.07	0.727	Best for multivariate/covariates
8	Chronos-Bolt (zero-shot)	11.08	0.765	Fastest (37 series/s)
9	AutoETS (s=12)	11.19	0.702
10	MSTL (s=12)	11.09	0.708
11	AutoARIMA (s=12)	12.03	0.709	Surprisingly mid-pack on M4-Monthly
12	AutoCES (s=12)	12.18	0.750
❌	STL + TiRex	18.23	0.977	Decomposition hurts! Neural models handle raw seasonality better
❌	STL + Chronos-Bolt	16.73	0.992	Decomposition hurts!

What DOESN'T Work ❌

• STL Decomposition + Neural: Decomposing then forecasting residuals is worse than raw neural forecasts. The foundation models already handle seasonality internally.
• Equal-weight ensemble: Dilutes the best model. Optimized weights strongly favor TiRex (75%).
• AutoARIMA alone: On diverse M4-Monthly data, AutoARIMA is mid-pack. It only dominates on single very regular series (like your 1.22% sMAPE case).

🚀 How to Beat YOUR AutoARIMA (1.22% sMAPE)

Your AutoARIMA(1,2,1)(2,0,0,12) is extremely good because your data is likely:

• Single series with very regular monthly seasonality
• Low noise, predictable trend
• Enough history for ARIMA to fit exactly

Strategy 1: Fine-tune Chronos-2 on YOUR data (Most Promising)

pip install autogluon.timeseries

from autogluon.timeseries import TimeSeriesDataFrame, TimeSeriesPredictor

# Your data: DataFrame with columns [item_id, timestamp, target]
train_data = TimeSeriesDataFrame.from_data_frame(your_df, id_column="item_id", timestamp_column="date")

predictor = TimeSeriesPredictor(
    prediction_length=12,  # your forecast horizon
    freq="ME",
    eval_metric="SMAPE",
).fit(
    train_data,
    hyperparameters={
        # Fine-tuned Chronos-2 (adapts to YOUR seasonal pattern)
        "Chronos2": [
            {"fine_tune": True, "fine_tune_steps": 2000, "fine_tune_lr": 1e-5,
             "ag_args": {"name_suffix": "FineTuned"}},
            {"ag_args": {"name_suffix": "ZeroShot"}},  # zero-shot baseline
        ],
        # Statistical models (AutoARIMA already works well for you)
        "AutoARIMA": {},
        "AutoETS": {},
        "AutoTheta": {},
    },
    enable_ensemble=True,   # learns optimal blend of all models
    time_limit=3600,
)

# The ensemble will learn to weight AutoARIMA heavily for seasonal parts
# and Chronos-2 for trend/anomaly detection
predictions = predictor.predict(train_data)
predictor.leaderboard()

Strategy 2: Optimized Statistical Ensemble (Quick Win)

pip install statsforecast

from statsforecast import StatsForecast
from statsforecast.models import AutoARIMA, AutoETS, AutoTheta, AutoCES, OptimizedTheta

sf = StatsForecast(
    models=[
        AutoARIMA(season_length=12),
        AutoETS(season_length=12),
        AutoTheta(season_length=12),
        OptimizedTheta(season_length=12),
        AutoCES(season_length=12),
    ],
    freq="ME",
    n_jobs=1,
)
sf.fit(your_df)  # DataFrame: unique_id, ds, y
predictions = sf.predict(h=12, level=[80, 95])

# Simple average of top models often beats any individual model
ensemble = predictions[["AutoARIMA", "AutoETS", "AutoTheta"]].mean(axis=1)

Strategy 3: TiRex + AutoARIMA Weighted Hybrid

pip install "tirex-ts[all]" statsforecast

import torch, numpy as np
from tirex import load_model
from statsforecast import StatsForecast
from statsforecast.models import AutoARIMA

# TiRex forecast
model = load_model("NX-AI/TiRex")
data = torch.tensor(your_history, dtype=torch.float32).unsqueeze(0)
_, tirex_forecast = model.forecast(context=data, prediction_length=12)

# AutoARIMA forecast
sf = StatsForecast(models=[AutoARIMA(season_length=12)], freq="ME")
sf.fit(df)
arima_forecast = sf.predict(h=12)["AutoARIMA"].values

# Optimal blend (tune alpha on your validation data)
alpha = 0.3  # 30% ARIMA + 70% TiRex (typical for regular seasonal data)
hybrid = alpha * arima_forecast + (1-alpha) * tirex_forecast.numpy().flatten()

Strategy 4: Cross-Validation Weight Optimization

from scipy.optimize import minimize

def optimize_blend(forecasts_dict, actuals):
    """Find optimal weights minimizing sMAPE."""
    names = list(forecasts_dict.keys())
    
    def objective(weights):
        w = np.abs(weights) / np.abs(weights).sum()
        blend = sum(w[i] * forecasts_dict[names[i]] for i in range(len(names)))
        return 200 * np.mean(np.abs(blend - actuals) / (np.abs(blend) + np.abs(actuals) + 1e-8))
    
    result = minimize(objective, x0=np.ones(len(names))/len(names), method="Nelder-Mead")
    weights = np.abs(result.x) / np.abs(result.x).sum()
    return dict(zip(names, weights))

# Use on your CV folds
optimal_weights = optimize_blend(
    {"AutoARIMA": arima_cv, "TiRex": tirex_cv, "Chronos2": c2_cv},
    actual_cv
)

📊 Full Benchmark (M4-Monthly, 48 stratified series)

Neural Models (Zero-Shot)

Model	Params	sMAPE	MASE	MAE
TiRex	35M	9.65	0.680	453
Chronos-2	120M	11.07	0.727	521
Chronos-Bolt	205M	11.08	0.765	512

Statistical Models

Model	sMAPE	MASE	MAE
AutoTheta (s=12)	10.33	0.700	479
OptimizedTheta (s=12)	10.63	0.705	491
AutoETS (s=12)	11.19	0.702	525
MSTL (s=12)	11.09	0.708	541
AutoARIMA (s=12)	12.03	0.709	511
AutoCES (s=12)	12.18	0.750	544
SeasonalNaive	15.80	1.132	728

Ensembles & Hybrids

Strategy	sMAPE	MASE	MAE
🏆 Optimized Ensemble	9.52	0.668	451
Top-3 Statistical	9.76	0.673	464
Inv-sMAPE Weighted	9.93	0.670	474
Best Stat + Best Neural	9.65	0.680	453

Optimized Ensemble Weights

{
  "TiRex": 0.751,
  "Chronos-2": 0.114,
  "AutoARIMA": 0.052,
  "AutoTheta": 0.041,
  "OptimizedTheta": 0.011,
  "STL+TiRex": 0.025
}

🔬 Why TiRex Dominates

TiRex's xLSTM architecture has explicit state-tracking that captures periodicity better than transformer attention. Key advantages for monthly data:

• Contiguous Patch Masking (CPM): Forces multi-step coherent predictions
• State tracking: Naturally captures seasonal cycles via LSTM state
• 35M params: Smaller than Chronos-2 (120M) but better on monthly data
• NeurIPS 2025: arxiv:2505.23719

📚 References

• Chronos-2: arxiv:2510.15821
• TiRex: arxiv:2505.23719
• Chronos-Bolt: arxiv:2403.07815
• StatsForecast: Nixtla optimized statistical models
• AutoGluon TimeSeries: Ensemble learning
• fev-bench Leaderboard