A Subspace approach to reduced rank time-series models

While reduced rank time-series models go back over 30 years, there is a renewed interest because of the now commonplace occurrence of high dimensional time-series. Here, for the first time, we characterize the two basic reduced rank vector time-series models in state space terms in a surprisingly simple way. This allows us to extend these models from vector AR to vector ARMA and we develop two new associated subspace fitting algorithms.