Reduced rank models for multiple time series

This paper is concerned with the investigation of reduced rank coefficient models for multiple time series. In particular, autoregressive processes which have a structure to their coefficient matrices similar to that of classical multivariate reduced rank regression are studied in detail. The estimation of parameters and associated asymptotic theory are derived. The exact correspondence between the reduced rank regression procedure for multiple autoregressive processes and the canonical analysis of Box & Tiao (1977) is briefly indicated. To illustrate the methods, U.S. hog data are considered.