Forecasting with Diagonal Multiple Time Series Models: An Extension of Univariate Models

Abstract

The authors discuss a special case of multiple time series models in which the autoregressive and moving average parameter matrices are diagonal. These models, called MTS-D, are appropriate if the random shocks which drive the series are only contemporaneously correlated. The flexibility and usefulness of this approach are illustrated in the context of a competitive market situation with five sales series, where individual components follow different univariate time series models. Theoretical as well as empirical justifications for expecting more precise parameter estimates are given. Forecasts from the model compare favorably with those from the univariate models.