Bayesian Analysis Of Financial Econometric Unit Root And Cointegration Models Based On Variance Gamma

Econometric model is one of the most common methods to study the dynamics problems of financial time series. The establishment of econometric model is generally based on the stationarity of time series, but in real market,the financial time series often do not have the characteristics of stability, so we need to test the stationarity of time series. As an important tool of testing time series stationarity, unit root test is always used. And cointegration test is often implied for judging long equilibrium between nonstationary variables. In many literatures, researchers often assume that financial data obey normal distribution or t distribution. However, the distributions of the real financial assets data often show these characteristics: excess kurtosis and volatility clustering, normal distribution or t distribution could not describe them well. Furthermore,variance gamma distribution can accurately describe the financial data by introducing suitable parameters. Although the introduction of variance gamma distribution can better fit the real data, it makes the classical unit root test and cointegration test more difficult. Especially, with a small sample, there will be more problems, such as low test efficiency, ultra-parameters, and the test statistic is difficult to determine. Bayesian method provides a convenient analytical framework and can make full use of financial data to overcome the above problems.In this paper, based on variance gamma distribution, Bayesian analysis of financial and economic models are conducted. Prior distributions of the model parameters were given, and the full conditional posterior distributions of the parameters were derived, Unit root test and cointegration test were conducted by means of Gibbs sampling.Lastly, an empirical study of Shanghai stock index and Shenzhen stock exchange index is carried out based an AR and linear Cointegration models.Bayesian research of unit root and cointegration tests are analyzed with the help of MCMC simulation method. The results indicate that Bayesian unit root and cointegration methods are effective tools to solve ultra-parameter and low test power in financial assets, and found that there is a long-term equilibrium relationship between the Shanghai Composite Index and Shenzhen component index, and both indexes have a positive change trend.