Comparison of tests for model specification in multivariate time series

In this paper we consider the problem of model specification and parameter estimation of a multivariate time series process. Four procedures are considered for model specification : the AIC criterion, the singular value decomposition of a certain block Hankel matrix, a test based on the columns of the observability matrix and a test based on the ratio of the determinants of the error covariance matrices from models of two different sizes. The estimation of the coefficients in the model is based on shift properties of three matrices: the block Hankel matrix, the observability matrix and the controllability matrix. A numerical example using a Monte Carlo experiment is presented for comparison of results. Copyright (C) 1998 IFAC.