A Bayesian Method for the Dynamic Regression Analysis

Abstract

A Bayesian time varying coefficient regression model with smoothness priors is introduced for inferring the dynamic relationship between two time series. Smoothness prior in the form of a Gaussian stochastic difference equation is imposed on the regression coefficient. The estimates of hyperparameters and the order of the difference equation are determined by maximizing marginal likelihood of the hyperparameters and using the minimum ABIC procedure. The estimate of the time varying regression coefficient is obtained by maximizing a posterior density of the coefficient. A numerical example and two simulation studies on the accuracy of the procedure are given. The model is applied to the analyses of the dynamic dependences of steel consumption on GNP for four countries.