The Optimality of General-Order Exponential Smoothing

This paper derives the class of nonstationary time-series representations for which exponential smoothing of arbitrary order minimizes mean-square forecast error. It points out that these representations are included in the class of integrated moving averages developed by Box and Jenkins, permitting various procedures to be applied to estimating the smoothing constant and determining the appropriate order of smoothing. These results further permit the principle of parsimony in parameterization to be applied to any choice between exponential smoothing and alternative forecasting procedures.