"algo-forecast-ensemble"

Ensemble Forecasting

Overview

Ensemble forecasting combines predictions from multiple models to reduce variance and improve accuracy. Simple average of 3-5 diverse models often outperforms the best individual model. Methods: equal-weight average, inverse-error weighting, stacking with a meta-learner. The "forecast combination puzzle" shows simple averaging is hard to beat.

When to Use

Trigger conditions:

• Multiple forecasting models are available and perform similarly
• Reducing forecast risk is more important than maximum accuracy
• Building a production pipeline that's robust to model failure

When NOT to use:

• When one model clearly dominates all others (just use that model)
• When computational budget only allows one model

Algorithm

IRON LAW: Simple Average Often Beats Complex Combination
The "forecast combination puzzle" (Stock & Watson, 2004): equal-weight
averaging of diverse models frequently outperforms sophisticated
weighting schemes. This is because weight estimation introduces noise
that offsets the theoretical gain. Start with simple average and only
move to weighted combination if you have abundant validation data.

Phase 1: Input Validation

Generate forecasts from 3+ diverse models (e.g., ARIMA, ETS, Prophet, ML-based). Ensure models are truly diverse (different assumptions/approaches). Gate: 3+ model forecasts available, models use different methodologies.

Phase 2: Core Algorithm

Simple average: ŷ_ensemble = (1/M) × Σ ŷ_m

Inverse-error weighting: w_m = (1/MSE_m) / Σ(1/MSE_j), ŷ_ensemble = Σ w_m × ŷ_m

Stacking: Train a meta-model (linear regression) that learns optimal weights from cross-validated individual model predictions.

Phase 3: Verification

Compare ensemble vs individual models on held-out data. Ensemble should: have lower average error AND lower maximum error (more robust). Gate: Ensemble RMSE ≤ best individual model RMSE.

Phase 4: Output

Return ensemble forecast with component model contributions.