Multivariate exponential smoothing: Method and practice

A multivariate extension of the familiar exponential smoothing procedure for forecasting univariate time series composed of level, seasonality and irregularity is presented. The updated estimates of the level, trend and seasonal effects of each of the component series are obtained as weighted averages of estimates derived by a univariate smoothing procedure and correction factors based on information gained from the other series. The forecasts are shown to be asymptotically optimal under particular state space models. The performance of the procedure is illustrated and compared to that of other univariate and multivariate forecasting procedures using two actual bivariate time series. The results are encouraging for the use of the procedure in practice.