SOME ROBUSTNESS PROPERTIES OF THE SIMPLE EXPONENTIAL SMOOTHING PREDICTOR

Abstract

Suppose we have the observations of a stochastic process {X_t} and we are required to predict its future values. There are many forecasting methods that might be used. However, it is difficult to decide which method we should adopt, since the accuracy of a forecasting method often depends on the properties of {X_t}, which can not be clearly known in many practical situations. In this paper, we investigate some aspects on robustness of the simple exponential smoothing method (SES). We will consider whether or not the forecasts provided by SES are reasonable not only when {X_t} is stationary but also when {X_t} deviates from a stationary process. For that purpose, we show prediction errors of the SES predictor for a wide class of stochastic processes, and we show comparisons of the prediction errors between this predictor and another predictor which is widely used.