A Unified Approach to Identifying Multivariate Time Series Models

Abstract

This article proposes a Bayesian procedure for simultaneous identification of the Kronecker indices and model parameters of a multivariate linear system. The model parameters include the starting values and innovations of the system so that the series considered may be co-integrated or non-invertible. The procedure uses some recent developments in stochastic search variable selection in linear regression analysis and Markov chain Monte Carlo methods in statistical computing. It also takes into consideration the row structure of a vector model implied by the Kronecker indices. Comparison with other existing methods is discussed. Simulated and real examples are used to illustrate the proposed procedure.