| Economic theory and empirical studies have shown that many important macroeconomic time series may exhibit nonlinear dynamic adjustment feature. The characteristics of this type of nonlinear dynamic adjustments can only be accurately modeled by nonlinear time series models. As one of common nonlinear time series models, the TAR model, since Tong (1983) proposed, its estimation and testing theories have been rapidly developed and perfected. Since Enders and Granger (1998) proposed the notion of Momentum TAR model (MTAR), the TAR model proposed by Tong (1983) is called self-excitation threshold autoregressive model (SETAR). Such that, this kind of models is divided into SETAR model and MTAR model. However, the academic literature has been no comparative study of these two types of models. Under populationary stable conditions, these two types of TAR models were compared systematically in this paper. On the nonstationarity theoretical research, based on CH (2001), Seo (2008) and KS (2006), this paper studied the unit root test theories of MTAR and SETAR models in depth. So the work of this paper can be illustrated in the following four parts:In research of comparison the MTAR with SETAR modeling, the paper conducted it from four aspects in detail, which is intuitive features, sample statistics moments, economic implications, and modeling characteristics. The study concluded that MTAR presents more sharpness than SETAR process; under conditions of stability, sample moment functions are steadily convergence to its population moments, but the specific formula of the moments function is unknown; SETAR model is generally applicable to the study of mean recovery of economic variables, and MTAR model can characterize the effectiveness of economic policy issues in real time, such as hedge; in modeling, this paper considered a weighted WSSR with a bootstrap critical value, which can effectively screening models, and improve modeling accuracy.To reveal the inapplicability of traditional unit root test methods under nonlinear conditions, using ADF, PP, KPSS, ERS unit root test methods, the paper do simulation works to test the testing size and power under different types of non-linear time series. The Conclusion is that non-linear effects, due to the different forms and their specific parameters, may act as a "sharpened" role or play a "hidden" effect, so it is necessary to develop the theory of nonlinear unit root test.In theoretical research of unit root test of MTAR and SETAR model, the third chapter expanded the unit root test theories of CH (2001) in2regime MTAR model to3regime MTAR unit root test, and derived the asymptotic distribution of test statistic; in the fourth chapter, unit root test theories of Seo (2008) in2regime SETAR model and KS (2006) in3regime SETAR model are extended to the case of estimating equation with the intercept term, and the asymptotic distributions of the test statistics are derived. In the Monte Carlo simulation study, in case of general and a structural change in mean, respectively, the paper simulated the testing size and power, using the asymptotic and bootstrap critical values for each statistic.In the empirical research, this paper studies the nonlinear dynamic adjustment of the exchange of RMB against the U.S. dollar by a three regime SETAR model. The main conclusion can be illustrated as follows. The detrending sequence of the exchange of RMB against the U.S. dollar presents a "BOI" area, which should be modeled by a3system SETAR model; in the short dynamic equilibrium term, there is a relationship between the relative purchasing power parity of RMB and the U.S. dollar, but the adjustment last for long period, and it is a strong persistent process; a greater proportion of RMB exchange rate is in the appreciation regime, you can interpret it as a appreciation pressure, and the speed of the mean reversion in the appreciation regime is faster, indicating resistance to appreciation pressures of the market and a foreign intervention force.
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