Practice✓ Mathematical
◆ The PatternCombining models for better accuracy
No single model wins everywhere. Ensemble forecasting combines diverse models — ARIMA, ETS, neural nets — for more robust predictions. The simplest approach (equal-weight average) is surprisingly hard to beat. More sophisticated methods include inverse-error weighting and stacking with a meta-learner.
// Interactive — ensemble vs individual forecasts
| Method | Approach | When |
|---|---|---|
| Simple Average | Mean of all forecasts | Default baseline — often the best |
| Weighted Average | Weight by inverse validation error | When model quality varies |
| Stacking | Train meta-model on forecasts | When interaction effects exist |
| Median | Median of all forecasts | When outlier models are present |
# Python — forecast ensemble import numpy as np # Simple average ensemble forecasts = [arima_pred, ets_pred, lstm_pred] ensemble = np.mean(forecasts, axis=0) # Inverse-error weighted errors = [mae_arima, mae_ets, mae_lstm] weights = [1/e for e in errors] w_sum = sum(weights) ensemble_w = sum(f*w/w_sum for f,w in zip(forecasts, weights))
Pattern bridge: Forecast ensembling is the time-series version of ensemble methods from statistics. In markets, portfolio diversification applies exactly the same principle — combining uncorrelated assets (models) reduces risk (error).