Theory And Applications Of SETAR Model And Shocks Effects

It has been proved that most of macroeconomic time series is a nonlinear process. The nonlinear model is preferred because it can describe the asymmetric adjustment behavior of macroeconomic time series. Therefore, the theory and method of nonlinear model has become an important part of macroeconometrics. However, there are two shortcomings on parameter estimation of SETAR model which is a particular popular nonlinear model in empirical research.. It can be described as the following:firstly, the estimation of autoregressive order of SETAR model is still using linear methodology, which has not been proved correctly or not; secondly, the asymptotic theory and small sample property of estimator of delay parameter, threshold value and coefficients in SETAR model building on the known autoregressive order. In this issue, we improve the two shortcomings by Monte Carlo simulation. The simulation result shows that:(1) the estimator's accuracy of autoregressive order in high order SETAR model is poor and different methods produce quite different estimation results. According to our simulation results, we think that one should use information criterion when the autoregressive order does not exceed two and use PACF otherwise. (2) In the case of autoregressive order unknown, the overestimated autoregressive order don't have significant effect on the other parameter estimation in SETAR model. However, the delayed parameter's region will be narrowed which will have direct effect on the estimation of delayed parameter's accuracy when we underestimate the autoregressive order. Hence, we suggest the strategy: overestimation rather than underestimation. One can use PACF at first, then re-estimate the autoregressive orders by linear methodology after having estimated all of parameters in SETAR model, which can improve the accuracy of autoregressive order's estimator. Moreover, we proved this strategy is feasible and reasonable.As Dijk et al (2007) points out that it generally is difficult, if not impossible, to fully understand and interpret time series models by considering the estimated values of the model parameters only. It can be very helpful to consider the effects of shocks on the future patterns of the time series variable. Therefore, the theory of shocks'effects develops with the time series theory which is the base of shocks' effects theory. After 1980s, non-stationary and nonlinear time series models'development promote the forming of shock's effects theories in these two time series proceesses. This issue found there are two shortcomings after analysising shock effects' theories. Firstly, the estimation of variance ratio statistic which be used to measure the persistent shock effect exists bias in small sample. Secondly, there isn't reasonable algorithm to compute the parameters of SEITMA model which be used to identify the persistent shocks, because the estimator of parameters of SEITMA model is the solution of minimizing a non-continued object function which has not close expression and the property is unknown. Hence, this issue deeply researches these two shortcomings and the contributions as follows:(1) we propose a new method to estimate the variance ratio statistic, which is consistence and have not bias and have excellent performance in small sample. Moreover, this new method has a good apply values because it's easing for computing and understanding. (2) this issue uses three popular non-continued object function global minimizing algorithms such as generalized pattern search, simulated annealing and genetic algorithm to solve the problem about the estimation of SEITMA. We found that genetic algorithm is the best algorithm for computing the estimator of the parameters of SEITMA model. Moreover, we found the property of these estimator in small sample based on genetric algorithm.As the examples of empirical research, at first, we study two cases which are the existence and importance of persistent shocks' in Chinese GDP time series and the identifying of persistent shocks in China's economic growth in the issue. The study of identifying of persistent shocks is based on SEITMA model in which the parameters' estimator be computed by genetic algorithm, while the analysis of existence and importance measure of persistent shocks'which based on B-N decomposition and variance ratio statistic which be computed by the new method proposed by this issue. Finally, this issue studies the property of asymmetric adjustment behavior in Chinese economic growth by using SETAR model, and the studies of dynamic property such as asymmetry of shocks'effects and so on in Chinese economic growth,which based on generalize impulse response function. These empirical studies' results match the style facts of Chinese economy and have plenty of implies of economics and economic policies.