Holt-Winters

Learn how to use Holt-Winters exponential smoothing for forecasting.

Understanding Holt-Winters

Past data is compressed using exponential smoothing via the Holt-Winters method to anticipate typical values for the present and the future. Exponential smoothing means smoothing a time series using an exponentially weighted moving average (EWMA). Like a rolling mean, it can be used on past data to make it smoother but also to make forecasts for future values.

An exponentially weighted moving average FtF_t is calculated as Ft=αxt+(1α)Ft1F_t = \alpha x_t + (1-\alpha) F_{t-1} for an additive model and as Ft=αxt(1α)Ft1F_t = \alpha x_t (1-\alpha) F_{t-1} for a multiplicative model in which α\alpha is a smoothing constant.

The Holt-Winters method includes both a slope smoothing component to take the trend into account and a seasonal smoothing. So the model gets three equations—one for the level, one for the trend, and one for seasonality. Furthermore, each of these three equations has two versions—additive and multiplicative.

  • Level

    • Additive: ...