Research And Application Of Cointegraton Analysis Based On MCMC

With the widely use of time series technologies, cointegration analysis, as a technology to deal with non-stationary time series, is now welcomed by researchers, and it gives rise to deep theoretical studies and shows a broad application prospects.The cores of cointegration analysis lie in estimation of cointegration vector and the test of cointegration relationship. The commonly used methods for parameter estimation are OLS estimation and maximum likelihood estimation. The commonly used cointegration test methods include EG method and Johansen method, however, these methods are on the basis of large number of sample observations. In this paper, under the condition of small samples, we propose a cointegration analysis method based on MCMC simulation, this method can make full use of the priori information of the samples when estimate the parameters and it can simulate the critical value, those properties add great flexibility to cointegration analysis.The study focuses on the following aspects:Firstly, we introduce the concept of cointegration and the current research methods, induing Unit Root Process, VAR with unit root,cointegration and Error Correction Model, estimation of cointegration vector, and the cointegration test with given cointegration vector.Secondly, considering that the computation of the eigenvalue which are used for Johansen cointegration test is complex, we introduce the Bayes method based on MCMC sampling to estimate the eigenvalue,then we apply Trace Test and Max-eigenvalue test based on the Johansen cointegration test to examine the existence of cointegration relationship. The test result is in accord with the test result when the cointegration vector is given, and it verifies the reliability and effectiveness.Thirdly, we get the posterior distribution of the cointegration vector by supposing that the stochastic term of the model is normal distribution, and then we can obtain the estimation of cointegration vector according to MCMC simulation. The estimation result is more accurate for we make use of the samples information during MCMC simulation. We call Win BUGS to get the critical values for statistics.Finally, we establish a cointegration forecasting model to study the demand trend of Chinese monetary based on MCMC.The result shows that this method has a favorable forecasting outcome.