The Research And Application Of The Smooth Transition Autoregression

As we know, the statistical inference about the linear model has been developed to mature, which is discussed based on the perfect mathematical theory, relatively. Since that, the main analysis approach is to make use of linear time series, but the further research pointed out the linear model leads into biased result relative to the actuality, even big errors, on the economic and financial phenomena. Due to that, STAR model, short for the smooth transition autoregression, has been developed as a special nonlinear time series model step by step, the parameters in this model, is very significant for economics analysis. Its birth and development is intensively related to exchange rate theory and business cycle. The first formal literature is Granger and Ter?svirta (1993); after that, by a great deal of researches, it is reported that it is very fit for the characteristics of mean reverting on business cycle, exchange rate and unemployment rate.The paper introduces the background about the nonlinear time series model and STAR model. The following is to introduce the specification, estimation and hypothesis test about it. Further more, it makes analysis of the test for linearity to nonlinearity, pointing out why the test is low power and how to improve it. At last, the author does a good research about whether the exchange rate of RMB to U.S Dollar is consistent to Purchase Power Parity, via the threshold cointegration with ESTAR.The innovation of the paper focus on the test for linearity to nonlinearity in STAR, so the conclusion is the traditional approach to the test is low power, by the mathematical analysis and simulation on computer, and AIC or Modified AIC can improved it, which is advised by the author.The applying for the threshold cointegration with ESTAR, is a special regression advised by author to avoid the spurious regression on the direct using ESTAR, and meanwhile, it can dig out the characteristics of the local disconintegration and overall conintegration about the time series, and dynamic nonlinear process for the convergence to overall conintegration.