Time Series Forecasting

State of the Art Research Report

The Great Bifurcation of
Time Series Forecasting

2025 is defined by a schism: The industrialization of massive Foundation Models (TSFMs) vs. the pragmatic dominance of Statistical Ensembles.

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Foundation Models (TSFMs)

Treats time series as a "language." Trained on billions of tokens to learn universal patterns.

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Tokenization: Patching (TimesFM) or Quantization (Chronos) to bridge the modality gap.
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Architecture: Transformers & Linear-Complexity Models (Mamba).
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Strength: Zero-shot generalization, cold-start problems.

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Statistical & GBDTs

The "Statistical Renaissance." Radical software engineering (Numba/JIT) meets feature engineering.

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Speed: StatsForecast (Nixtla) is 500x faster than Prophet.
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Dominance: Kaggle & M6 Competition winners (XGBoost, LightGBM).
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Strength: Tabular data, complex exogenous variables, accuracy.

Architectural Frontier

How deep learning handles continuous time.

Chronos (Amazon)

Quantization

Treats time series as a language task by binning continuous values into discrete tokens.

Output: Probabilistic distribution (good for uncertainty).

TimesFM (Google)

Patching

Uses Patching to aggregate time steps into semantic tokens, reducing sequence length.

Output: Direct multi-horizon forecast.

Mamba (SSM)

Linear Complexity

Revisits RNNs/State Space Models to process massive history windows with O(L) complexity.

Output: Efficient long-context processing.

The Crucible of Truth

In high-stakes competitions like the M6 Financial Forecasting Competition, complex models often fail against simple baselines due to low signal-to-noise ratios.

M6 Finding

Deep Learning models failed to beat simple equal-weighted ensembles. Risk management > Forecasting accuracy.

Kaggle Finding

Feature Engineering + XGBoost/LightGBM is the "Winning Formula" for tabular data.

Zero-Shot vs. Trained Performance (Normalized Error)

TSFMs (Foundation Models) excel at "Zero-Shot" but optimized Statistical Ensembles often win when fine-tuned.

From Prediction to Action

The frontier is Prescriptive Analytics via Reinforcement Learning.

The Old Pipeline

Forecast → Optimize

1. Model predicts Demand (y)

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2. Solver calculates Order (x)

Minimizes MSE, which may not align with minimizing business *cost*.

The 2025 SOTA

End-to-End RL

Agent observes State ($S_t$) → Outputs Action ($A_t$)

Inventory Reward Function: $$R_t = p \cdot \min(d_t, I_t) - h \cdot I_t - \pi \cdot \max(0, d_t - I_t)$$

Directly optimizes Profit. Used by Amazon/Instacart for inventory placement.