HoltWintersETS

HoltWintersETS is a family of time series forecasting models built on the exponential smoothing framework that incorporates error, trend, and seasonality components. The approach extends simple Holt-Winters methods by allowing different combinations of additive or multiplicative structures for each component, and by often including options for damped trends. It is commonly described within the ETS (Error, Trend, Seasonality) modeling framework, where a model is denoted by the triple of component types (for example, additive or multiplicative error, trend, and seasonality).

In HoltWintersETS, the observed series is assumed to follow a state-space form with level, trend, and seasonal components, plus a stochastic error term. The possible configurations include variations such as no trend, additive trend with or without damping, and seasonality that is either additive or multiplicative or absent. The multiplicative forms are appropriate when the seasonal fluctuations grow with the level of the series, while additive forms suit constant seasonal swings. The model selection process (in many implementations) compares several ETS configurations and selects one based on information criteria or forecast accuracy.

Estimation is typically performed through maximum likelihood or minimum-sum-of-squares procedures, often implemented via a Kalman filter to handle the latent state components. Once fitted, HoltWintersETS provides in-sample fitted values, residuals, and out-of-sample forecasts with corresponding prediction intervals. It is suitable for data with clear seasonal patterns and a stable seasonal structure, and it is widely used in business forecasting, inventory planning, and demand projection. Limitations include sensitivity to structural breaks and non-stationary changes, and the need to choose an appropriate seasonal period.