Forecasting
From models to predictions. Point forecasts, interval forecasts, accuracy metrics, exponential smoothing, and Prophet.
Point vs. Interval
- Point forecast — single best guess; simple but incomplete
- Interval forecast — range quantifying uncertainty; essential for decisions
Prediction Intervals
Forecast uncertainty grows with horizon. For a random walk, intervals fan out as √h.
Error Metrics
Measured on a held-out test set the model never saw.
Simple SES
Assign exponentially decreasing weights to past observations. One parameter α — equivalent to ARIMA(0,1,1).
Holt & Holt–Winters
- Holt: adds trend component (β); no seasonality
- Holt–Winters additive: constant seasonal variation (γ)
- Holt–Winters multiplicative: growing seasonal swings
Prophet
Decomposes into trend + seasonality + holidays. Handles missing data and outliers automatically; minimal tuning.
Walk-Forward CV
Standard k-fold CV leaks the future. Instead, train up to t, evaluate on t+1…t+h, then advance.
Expanding vs. Rolling
Ensemble Forecasting
Combining multiple forecasts almost always outperforms any single model. Equal-weight averaging is a strong baseline.
Choosing a Method
- Short series, no seasonality → SES or ARIMA(0,1,1)
- Trend present → Holt’s linear
- Trend + seasonality → Holt–Winters or SARIMA
- Business series, holidays → Prophet
- Best accuracy → Ensemble of the above
What you learned
Forecasting requires prediction intervals, proper hold-out evaluation, walk-forward CV, and combining methods. No single model always wins.