Exponential Smoothing Models

Exponential Smoothing models are a broad class of forecasting models that are intuitive, flexible, and extensible.

Members of this class include simple, single parameter models that predict the future as a linear combination of a previous level and a current shock. Extensions can include parameters for linear or non-linear trend, trend damping, simple or complex seasonality, related series, various forms of non-linearity in the forecasting equations, and handling of irregular time series.

Exponential smoothing assumes that a series extends infinitely into the past, but that influence of past on future, decays smoothly and exponentially fast. The smooth rate of decay is expressed by one or more smoothing constants. The smoothing constants are parameters that the model estimates. The assumption is made practical for modeling real world data by using an equivalent recursive formulation that is only expressed in terms of an estimate of the current level based on prior history and a shock to that estimate dependent on current conditions only.The procedure requires an estimate for the time period just prior to the first observation, that encapsulates all prior history. This initial observation is an additional model parameter whose value is estimated by the modeling procedure.

Components of ESM such as trend and seasonality extensions, can have an additive or multiplicative form. The simpler additive models assume that shock, trend, and seasonality are linear effects within the recursive formulation.