Complete modeling of multidimensional noise as a multivariate autoregressive process

Abstract

A new method for multivariate autoregressive modeling of a vector time series is described, which has an advantage in guaranteeing less-biased estimation in a least-squares sense by ensuring orthogonality between the components of a residual vector. An expression for a multivariate autoregressive model with a zero-lag coefficient matrix is derived theoretically and utilized for the modeling based on a weighted least-squares procedure. Model parameters such as regression matrices and residual matrix are determined recursively for each value of order by using the LWR algorithm. It is shown that the present modeling differs from the ordinary one in estimating open-loop properties, though these modeling are equivalent for closed-loop estimates.