Bayesian Analysis Of Financial Econometric Unit Root And Cointegration Models

The financial and economic time series models are constructed on the basis of the null hypothesis that the series are stationary, however, there are almost nonstationary series in practice. As an important tool of testing time series stationarity, unit root test is always used, and cointegration test is also often implied for judging long equilibrium between nonstationary variables. It is well known that the classical methods for unit root and cointegration test require large samples, and there exsits ultra-parameter problems in models, which cause the seriously biased estimation. In order to solve these problems, this paper deals with unit root and cointegration test from Bayesian perspective, improving the power of tests and solving the problem of parameters'estimation.Based on Bayes Theorem, Bayesian analysis of univariate time series and multivariate time series are conducted with AR(1),AR(p) and restricted VAR(p),unrestricted VAR(p) models, repectively, obtaining the methods of Bayesian unit root test; then combined with VAR model, Bayesian cointegration tests of bivariate and multivariate series are carried out, producing Bayesian linear cointegration test which is a variety of classic EG cointegration, and a method of Bayesian nonlinear cointegration test. The comparison between classic cointegration and Bayesian cointegration test is proceed by a set of Monte Carlo simulation, which shows that Bayesian test power exceeds classic one. Meanwhile, the parameters'Bayesian statistical inference on designed prior distribution, and MCMC computational procedure devising is conducted, which is necessary to unit root and cointegration analysis of financial and economic time series.Lastly, an empirical study of Chinese residents'consumption price indices is carried out based on VAR and nonlinear Cointegrating VAR models. Combined with Gibbs sampling, Bayesian research of unit root and cointegration tests are analyzed. The results indicate that the Bayesian unit root and cointegration methods are effective tools to solve ultra-parameter problem in VAR and CVAR models, supply a gap for the poor power of small samples in financial and economic series and improve the precision of prediction.