A dynamic factor model

This paper attempts to find the possibilities of simplifying a multiple time series. We consider a dynamic factor model, Z(t) = Sigma(i=1)(m), Lambda(i)X(t-i) + Gepsilon(t), where Z(t) is a k-dimensional Gaussian stationary time series, X-t is an unobservable r-dimensional factor series (K greater than or equal to r) and epsilon(t) is a (K - r)-dimensional white noise series, fully independent of {X-t}. The model is for reducing the dimension of time effect of the series, because the error term is independent of time. This article starts with an example showing that two independent AR(1) series can be generated by one series under this model. Mathematical properties of the model are studied. Its relations with other time series models are also discussed.