algo-forecast-exponential

# Exponential Smoothing ## Overview Exponential smoothing assigns exponentially decreasing weights to past observations. Three variants: Simple (SES, level only), Holt (level + trend), Holt-Winters (level + trend + seasonality). ETS framework (Error-Trend-Seasonality) provides a unified statistical model. Fast, interpretable, and competitive with complex models for short horizons. ## When to Use **Trigger conditions:** - Quick forecasting with minimal configuration - Short-horizon forecasts (1-2 seasonal cycles ahead) - Data with clear level, trend, and/or seasonal components **When NOT to use:** - For long-range forecasts (uncertainty accumulates too fast) - When external regressors are important (use regression or ML models) ## Algorithm ``` IRON LAW: Smoothing Parameters Control the Bias-Variance Trade-Off α (level), β (trend), γ (seasonality) range [0,1]. - α near 1: react quickly to changes, noisy forecasts (high variance) - α near 0: smooth forecasts, slow to adapt (high bias) Optimize via minimizing MSE on training data (or use information criteria). Never hand-pick smoothing parameters without validation. ``` ### Phase 1: Input Validation Identify components: level only (SES), level+trend (Holt), level+trend+seasonality (Holt-Winters). Determine: additive vs multiplicative trend/seasonality. **Gate:** Component structure identified, seasonal period known. ### Phase 2: Core Algorithm **Holt-Winters (additive):** 1. Initialize: level₀ = mean(first season), tren...