Reduced-Rank Regression Model With Autoregressive Errors

Abstract

The classical multivariate regression methods are based on the assumptions that (i) the regression coefficient matrix is of full rank and (ii) the error terms in the model are independent. In Chapters 2 and 3, we have presented regression models that describe the linear relationships between two or more large sets of variables with a fewer number of parameters than that posited by the classical model. The assumption (i) of full rank of the coefficient matrix was relaxed and the possibility of reduced rank for the coefficient matrix has produced a rich class of models. In this chapter we also weaken the assumption (ii) that the errors are independent, to allow for possible correlation in the errors which may be likely with time series data. For the ozone/temperature time series data considered in Chapter 3, the assumption of independence of errors appears to hold.