A principal component approach to dynamic regression models

In this paper we introduce a dynamic regression model that states how an output is related to an input allowing future values forecasting. The basic tools to set up this model are the orthogonal decomposition of a discrete time stochastic process by means of its principal components analysis, and the linear regression performed on the principal components of input and output processes. The behaviour of this model is empirically studied on real data, showing that low forecast errors are obtained by using this model. A comparison between such a model and a transfer function one, for a particular two time-series case, is discussed.