Since The Regression Model Stationary

A unit root test is the base of building the ARMA model, ARIMA model and the cointegration analysis among variables. As a special hypothesis test, the reliability studying of the unit root test and how to find a reliable test method or statistics has become one of a importance issue in time series analysis.In 2006, a Japanese scholar proposed a procedure of unit root testing based on the minimum information criterion. This method test unit root through the model selecting. Under the discussion of statistical property of AR(1) model, this paper proposed a detecting procedure for unit root test of AR(1) model by use of the minimum information criterion method. The method in this article has some advantages compare to the conventional method of hypothesis test. At the same time the method of information criterion and DF test method have used in simulated study. The results have showed the method of model selecting based on the minimum information criterionis is an effective method in unit root test. Furthermore, the method of unit root test based on the minimum information criterion is simpler and more reliable than the DF test.For the nonlinear autoregressive model denoted by stochastical difference equation, the model exist a stable solution under what model structure and parameter condition, this question has important significience in modeling, estimating of paramater and property analysising of nonlinear time series analysis. By the results that have proved we know that the stationarity of the nonlinear autoregressive model was determined by the ergodicity of corresponding markov chain of which was defineded by the nonlinear time series in relevant. In some condition, the ergodicity of markov chain can be considered as the stationarity of corresponding stochastical system.In the study of stationarity and ergodicity of nonlinear autoregressive model, it has been obtained the plenty of the study results for the additive noise model and random conditional variance model of functional type by use the knowledge of Markov chain in a general state space. In addition, the question of geometrical ergodicity has been studied thoroughly for some special nonlinear autoregressive model, such as ARCH and GARCH model.This paper consider the ergodicity and geometrical ergodicity of a general nonlinear autoregressive model. Under the study of the nonlinear autoregressive model with additive noise model and random conditional variance model of functional type, author generalized the study results of ergodicity and geometrical ergodicity to the general nonlinear autoregressive model and obtained the the sufficient condition of geometrical ergodicity under the compress condition and noncompress condition. The work generalize the study results of former in this field.