Exponential Smoothing: A Prediction Error Decomposition Principle

In the exponential smoothing approach to forecasting, restrictions are often imposed on the smoothing parameters which ensure that certain components are exponentially weighted averages. In this paper, a new general restriction is derived on the basis that the one-step ahead prediction error can be decomposed into permanent and transient components. It is found that this general restriction reduces to the common restrictions used for simple, trend and seasonal exponential smoothing. As such, the prediction error argument provides the rationale for these restrictions.