Study On Several Application Problem Of Co-Integration Model Based On Monte Carlo Method

Since the co-integration phenomenon was found by Engle and Granger, co-integration theory has been widely used, from financial industry to agriculture; from macro-economy to microeconomics; from capital market to monetary market. However, because of lacking of in-depth understanding of related theoretical basis and mathematical model and we use it with strong subjectivity, leading to some mistakes when we use this theory.This article reviewed co-integration theory and the literature on its applications. Introducing correlation theory of co-integration, including the stationary of time series and unit root test; vector autoregression model; co-integration and error correction model and Monte Carlo simulation experiment, make a theoretical groundwork for the full text.Firstly, we analyzed the occasion of missing co-integration item in VAR model. In VAR system, although by difference, Variables and VAR system can be stable, but if a co-integration relationship exists, only by difference, the VAR system will be B-Bias. In this part, by Monte Carlo simulation experiment, we compared the validity of parameter estimation when co-integration exist, between VAR with A first order differential form and the error correction model correctly confirmed. The study found A first order differential VAR system with omitting the co-integration item, would lead a biased model, which will cause the invalid statistical inference of Granger causality tests, variance decomposition; and so on. It indicates to modeling for time series data, it is necessary to test the stationarity and co-integration relationship.Then, we discuss the importance of proper identification on DGP for Johansen and Juselius co-integration tests. Based on the Monte Carlo simulation experiment, we analyzed the number of co-integrated vector and the unbiasedness of coordination coefficient for Johansen and Juselius co-integration tests, when the DGP was wrongly setting. Compared the test results when DGP is correctly setting with wrongly setting, the result is no mater the number of co-integrated vector and the unbiasedness of coordination coefficient was biased when using Johansen and Juselius co-integration tests. It indicates when we test the co-integration relationship with Johansen and Juselius co-integration test method, correctly recognize the DGP is important.Finally, we compared Engle-Granger test、Johansen and Juselius co-integration test and ADL test. From the theoretical perspective, Elaborated the advantage of Johansen and Juselius co-integration, when compared to Engle-Granger test.we discussed the co-integration relationship when Weak exogenous variables exist. by Monte Carlo simulation experiment we find, when test the co-integration relationship with weakly exogenous variables, the ADL test had a higher power than Engle-Granger test and Johansen and Juselius co-integration test. Especially the occasion of small sample, the advantage is more obvious. But if weakly exogenous not exist, the ADL test had a lower power than Engle-Granger test and Johansen and Juselius co-integration test, Especially the occasion of small sample, this trend is more obvious.By the end of the article, full text was summarized, and the future study direction was pointed.