Smoothing
Smoothing methods are weighted averages of past observations, with the weights decaying exponentially as the observations get more remote. Exponential smoothing is a family of methods that vary by their trend and seasonal components.
| Seasonal Component | |||
|---|---|---|---|
| Trend Component | None | Additive | Multiplicative |
| None | Simple Smoothing | ||
| Additive | Holt’s linear method | Additive Holt-Winters’ method | Multiplicative Holt-Winters’ method |
| Additive Damped | Additive damped trend method | Holt-Winters’ damped method | |
Simple exponential smoothing models have no seasonal or trend components.
Holt’s linear method extends SES with a trend component.
Holt’s linear trend produces a sloped, but straight line. Research has shown that the assumption of a constant trend in the forecast tends to overshoot. Gardner and McKenzie added a damping parameter ϕ to reduce the forecasted trend to a flat line over time.
The Holt-Winters method extends Holt’s method with a seasonality component, s(t), for m seasons per period. There are two versions of this model, the additive and the multiplicative. The additive method assumes the error variance is constant, and the seasonal component sums to approximately zero over the course of the year. The multiplicative version assumes the error variance scales with the level, and the seasonal component sums to approximately m over the course of the year.