Holt-Winters exponential smoothing, also called triple exponential smoothing, forecasts time series by modeling level, trend, and seasonality together. It suits data with recurring seasonal patterns, including monthly sales or daily stock prices, and offers additive and multiplicative seasonal forms for constant or changing seasonal variation. section 7.4.4 section 7.4.7
Choose the exponential-smoothing form according to the observed structure:
- Use simple exponential smoothing for data without a clear trend or seasonal pattern. section 7.4.4
- Use double exponential smoothing when the series has a trend but no seasonal pattern. section 7.4.4
- Use Holt-Winters when both trend and seasonal variation matter; specify additive seasonality for constant variation or multiplicative seasonality for changing variation. section 7.4.4 section 7.5
Exponential smoothing applies exponentially decaying weights to past observations rather than explicitly modeling the underlying data-generating structure. In Python, statsmodels can fit the model with chosen trend, seasonal, and seasonal-period settings. Evaluate fit with AIC and BIC, then compare forecasts with alternatives such as ARIMA; lower AIC and BIC indicate the better fit among the compared models. section 7.4.1 section 7.4.7 section 7.4.5
>>> hw_model = ExponentialSmoothing(train, >>> trend = 'add', >>> seasonal = 'add', >>> seasonal_periods = 5).fit()
Fit an additive Holt-Winters model with statsmodels by selecting additive trend and seasonality and setting a five-observation seasonal period. section 7.4.7
Apple closing-price forecast
A Holt-Winters model forecasts Apple closing prices through April 2024 from prices observed between October 1, 2023, and April 30, 2024. The plotted Holt-Winters forecast is slightly more accurate than the corresponding ARIMA forecast. section 7.4.7
