Prediction by Exponentially Weighted Moving Averages and Related Methods

SUMMARY The mean square error of prediction is calculated for an exponentially weighted moving average (e.w.m.a.), when the series predicted is a Markov series, or a Markov series with superimposed error. The best choice of damping constant is given; the choice is not critical. There is a value of the Markov correlation ρ 0 below which it is impossible to predict, with an e.w.m.a., the local variations of the series. The mean square error of an e.w.m.a. is compared with the minimum possible value, namely that for the best linear predictor (Wiener). A modified e.w.m.a. is constructed having a mean square error approaching that of the Wiener predictor. This modification will be of value if the Markov correlation parameter is negative, and possibly also when the Markov parameter is near ρ 0.