Unit Root Test And Empirical Research Based On Estar Process

In recent years,the development model of Chinese economic has been transformed and upgraded,and the speed of economic development has been transformed from high-speed to medium-high-speed.Many macroeconomic variables show adjustment characteristics and obvious nonlinear fluctuations.So it has become one of the main methods in the study of time series by using the nonlinear time series model.To avoid spurious regression,It's necessary to judge whether the time series is stationary or not before modeling.The traditional unit root test methods are proposed for linear models,which are no longer applicable to the most widely used nonlinear models nowadays.It is easy to over-accept the assumption of non-stationary time series and cause invalid tests.Furthermore,the unit root test based on the nonlinear ESTAR model usually assumes that the residual obeying the white noise sequence.So the paper study the unit root test of ESTAR model and constructs the empirical likelihood ratio statistics when the residual obeying white noise process and GARCH process,and proves their non-degenerate asymptotic distribution.Compare with the KSS statistic,the empirical likelihood ratio statistic has higher test efficiency.Based on the basic theory of unit root test and the stationary ergodicity of ESTAR model,the linear auxiliary equation of unit root test of ESTAR model is obtained by Taylor expansion.In the third chapter,the paper study the ESTAR model when the residual obeying the white noise process,and creatively proposes empirical likelihood ratio statistic l1(?),and it's asymptotic distributions are derived.Compare with KSS test,Critical value Mento Carlo simulation shows statistic l1(?)has higher test efficiency.Considering some time series are time-varying,we suppose the residual of ESTAR model obeying GARCH process,and proposes empirical likelihood ratio statistic l2(?),and it's asymptotic distributions are derived based on the third chapter.Statistic l2(?)also has higher test efficiency compare with KSS test.The paper proposes the Bootstrap method of empirical likelihood ratio statistic based on ESTAR-GARCH model,the rationality of the method is proved theoretically.The result of simulation shows that the Bootstrap method has higher test efficiency than the critical value method under small-sample.Finally,the empirical study of SSE illustrate that the model based on empirical likelihood ratio test have the best fitting and predicting result,which further proves that this statistic has superior testing efficiency.