A Bayesian Analysis of Unit Roots and Structural Breaks in the Level and the Error Variance of Autoregressive Models of economic series

Abstract

In this paper, a Bayesian approach is suggested to compare unit root models with stationary autoregressive models when both the level and the error variance are subject to structural changes (known as breaks) of an unknown date. Ignoring structural breaks in the error variance may be responsible for not rejecting the unit root hypothesis, even if allowance is made in the inferential procedures for breaks in the mean. The paper utilizes analytic and Monte Carlo integration techniques for calculating the marginal likelihood of the models under consideration, in order to compute the posterior model probabilities. The performance of the method is assessed by simulation experiments. Some empirical applications of the method are conducted with the aim to investigate if it can detect structural breaks in financial series, especially with changes in the error variance.