Exponential Smoothing as a Special Case of a Linear Stochastic System

Abstract

This paper derives a uniformly-sampled-autoregressive-moving-average (USAM) model for a second-order linear stochastic system, shows that exponential smoothing is a limiting case of the USAM model, and discusses the optimal value of the exponential-smoothing parameter and its sensitivity to mean-squared error of prediction. The USAM model is interpreted as a first-order system with first-order feedback; its limiting behavior explains why many business, economic, and quality-control systems are predicted well by exponential smoothing. The results are illustrated by examples of real-life data from IBM stock prices, and quality-control measurements of an automatic screw-machine operation.