Exponential Smoothing for Multivariate Time Series

Summary A method is presented for estimating the optimum weight matrix for the exponential smoothing and prediction of multivariate time series. A recursive version of the estimation equations is given. A variation allows the estimation to forget the remote past in order to follow a process in which the structure varies slowly with time. It is pointed out that the method generalizes to non-linear processes when the non-linear structure is known. The practicality of the method is demonstrated by a numerical simulation study.