Unit Root Test And Empirical Research Based On STAR Process

Unit root test is a very important research content in econometric,especially under the background of that the real financial time series are nonlinear,and mostly non-stationary series contains a unit root.Unit root test in the research of time series data is an essential step.The traditional unit root test is proposed based on linear model,nonlinear model of the unit test result is not very effective,and easy to cause too much to accept non-stationary assumption,that cause misjudgment.So the paper study the unit root test that be applied to nonlinear STAR model with more applications in fact.Considering the fact that when the STAR model is used to simulate the time series data,the residual term of the model is often subject to the GARCH process,and the paper constructed the test likelihood ratio test statisticl(?)on the basis of the former 's study.The likelihood ratio test statistic greatly improves the unit root test efficiency of the STAR model,and can effectively avoid the calculation of statistic estimation variance,the effective reduction the computational complexity and the stability of the estimated statistic is improved of the unit root test statistic for the LSTAR-GARCH model proposed by Lujun Wang(2014).In this paper,first of all,the story and theory of the unit root test are introduced.and then based on that Lujun Wang(2014)put forward the unit text statistics tNG in view of the LSTAR-GARCH model.In the third chapter,the paper creatively proposes empirical likelihood ratio test statistics l(?),and it's asymptotic distributions are derived.On the conditions of the time series variance time-varying characteristics(GARCH),the limiting distribution of tNG need to be taken into account in the derivation process variance,this will increase the instability and the computational complexity of tNG,and empirical likelihood ratio test statistics can effectively avoid the calculation of statistic estimation variance,thus improve the effect of the unit root test.In order to verify the theory of the third chapter,fourth chapter simulated and function comparison by Monte Carlo and the Bootstrap method,further explain the situation in the perspective of simulation.Furthermore,combined with China's Shanghai index stock data to carry on the empirical analysis,compare with fitting effects,explain empirical likelihood ratio test statistics for unit root test statistics have better fitting prediction result,and can provide investors with more accurate information.