Bayesian analysis of cointegrated vector autoregressive models
This thesis concerns econometric time series modelling of cointegrated multivariate systems using a Bayesian approach. The Bayesian approach has become increasingly attractive among researchers in the fields such as biology, though still only a relatively few econometricians use these techniques. Rather than theoretical aspects of Bayesian statistics or computational techniques, we illustrate how the Bayesian methods can be useful in analysing non-linear cointegration models. In the last ten years, non-linear time series models, such as regime switching models, have become popular among applied econometricians to analyse the business cycles, policy evaluation in specific macroeconomic issues and forecasting. Cointegration analysis has been influenced by the non-linearity so that cointegration models that allow regime switching or structural breaks have been analysed by many econometricians. Unfortunately, these nonlinear cointegration models tend to be complicated both in terms of estimation and testing. We consider in this thesis a Bayesian approach to (i) a linear cointegration model, (ii) a cointegration model with Markov regime switching, and (iii) a cointegration model with multiple structural breaks, and show how easily we can analyse these models without any substantial modification. Chapter 2 proposes a simple method for detecting cointegration rank using the Bayese factors, computed by the harmonic mean of the likelihood or Schwarz' Bayesian information criterion. Then we perform Monte Carlo simulations to compare three Bayesian methods (Phillips posterior information criterion, Kleibergen and Paap method, and one proposed method) for the cointegration rank. Provided we have enough large sample size, the Phillips' posterior information criterion gives consistent results, while the results by Kleibergen and Paap method depends on the prior hyperparameters that we specify. In Chapter 3, we develop the cointegration model that allows cointegration relationships to be switched on and off depending on the regime. Unlike the classical method that requires a two-step estimation, the Bayesian method provide a straightforward estimation and testing procedure. In Chapter 4, we consider cointegration model with multiple structural breaks in the level, trend and error covariance. The more general model with breaks in both the adjustment term and the cointegrating vectors are also presented. To date, there is no research that deals with a cointegration model with unknown multiple structural breaks in any subset of the parameters.