A bayesian multivariate nonstationary time series model for estimating mutual relationships among variables

The purpose of this paper is to propose a Bayesian multivariate stochastic model with latent nonstationary trends and seasonal components and show its use to determine the relationships among the variables. The model is expressed in state space form and the parameters of the model are estimated by maximum likelihood using a numerical optimization algorithm. The Kalman filter is used to compute the likelihood of the model and the information criterion AIC is used to select the best fitting model. The relationships among variables are examined in the frequency domain using estimated components. Japanese macroeconomic series are analyzed by our procedure.