Unit Root Test In The Smooth Transition Auto Regressive Model

As linear models gradually expose its limitations in the analysis of certain economic problems,nonlinear models are beginning to be widely used in macroeconomics and finance.As one of nonlinear model,smooth transition autoregressive(STAR)is more widely used because of its flexibility relative to the threshold autoregressive model.In the modeling process,it is important to set the model correctly,and the unit root test before modeling is the basis for correctly setting the model.The traditional ADF unit root test is based on the linear model,and still use this method to test the stationarity of nonlinear model may have problems such as low test efficiency.At present,the unit root test based on STAR is still not mature enough and needs further improvement.Therefore,this paper summarized the theories about STAR model's specification.Discussed the stationarity conditions of the ESTAR model and LSTAR model,summarized the KSS andt_LSTARunit root tests and simulated the two statistics'critical value.On the basis of the relevant theories of the STAR model's specification,the Wald unit root test method for joint testing of multiple coefficients under relaxed constraints is proposed.This method is more flexible and applicable than KSS test andt_LSTARtest.The progressive distribution of the Wald test is derived and the critical value of the statistic is given by simulation.Comparing these test methods'power by Monte Carlo simulation experiments,the proposed Wald test method is better than the KSS test andt_LSTARtest.The theory is applied in practice,and the real effective exchange rate index of RMB is selected for modeling analysis.The test shows that the first-order differential data is stable.When using the lag 5 data as the transfer variable,the data is nonlinear and suitable for LSTAR model.By establishing the AR(2)and LSTAR models for out-of-sample prediction,the prediction results show that the prediction effect of the LSTAR model is better than that of the AR model.The main innovations of this paper are as follows:1.Combed the existing theoretical,discussed the stationary condition of LSTAR model,simulated the critical value of KSS test statistic andt_LSTARtest statistic and the size performance of these two test.2.Under the condition of relaxing the constraints of the parameter c and?,the Wald unit root test statistic under the ESTAR and LSTAR model is proposed,and the proposed statistic is compared with the KSS test andt_LSTARtest respectively to verify the efficacy of the proposed statistic.