A Note on Exponential Smoothing and Autocorrelated Inputs

This paper considers the use of exponential smoothing to forecast time series which are compound processes containing both deterministic and random components. Recognition is given to the fact that modifications made in the simple smoothing formula to correct for one assumed component in the input series, such as a trend, interacts with the other series' components, and the total forecast error may be increased. The mean squared forecast error, using exponential smoothing, is compared when the random inputs are independently distributed and when they are autocorrelated. The latter case being commonly encountered in sales series. The characteristics of the smoothing procedure is examined when the input time series is geometrically autocorrelated and the range of values of the smoothing constant to minimize the forecast error is calculated.