Recursive identification, estimation and forecasting of multivariate time-series

Abstract

The paper describes a new, fully recursive method for identifying, estimating and forecasting multivariate (vector) time-series. Any low frequency (trend) components associated with each of the elements of the vector time-series are first removed by recursive, fixed interval smoothing based on generalised random walk (GRW) models; while the vector of perturbational residuals obtained from this 'detrending' step is then modelling as a vector AR or ARMA process. Finally the various structural models are combined to yield an overall multivariate, state-space model, which provides the basis for forecasting, using standard Kalman Filter methods. The practical utility of the approach is illustrated by a sales forecasting example.