A Study Of The Theory And Application Of STAR-GARCH Model

Economic and finance theory suggests that lots of important macroeconomic and financial time series exist the nonlinear characteristic, if you ignore this nonlinear characteristics, and using linear model for modeling analysis, only to find the wrong conclusions. So relax the linear restrictions, introduce the nonlinear method, which is benefit for the analysis of the macro economic and financial, with the development of computer technology, nonlinear model is more widely applied. In the frontier and hot issue of nonlinear econometric, as a result of the test and estimation theory maturity and operability, and stronger explanatory and predictive power of economic reality, the smooth transition autoregressive (STAR) model has been widely used. However, the STAR model only describes the nonlinear characteristics of conditional mean in macroeconomic and financial time series, in fact, the nonlinear characteristic of the part of the macroeconomic time series, and most of the financial time series is not only reflected in the conditional mean of the sequence, also will be showed on the conditional variances. In describing the nonlinear characteristics of the conditional variance model, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model is the most popular, which is able to capture the conditional variances time-varying characteristics of the sequence. Therefore, in view of the conditional mean and variance of nonlinear characteristics in the economic and financial time series to establish STAR-GARCH model has become the forefront research on economic and financial problems. As a result of the maturity of the related test and estimation for STAR-GARCH model, the model is also widely used. But the unit root test of time series which follows the STAR-GARCH model and forecast of the STAR-GARCH model are not yet discussed, there are some misunderstandings on the model application. This paper carried out the research; focus on the unit root test of time series which follows the STAR-GARCH model and the forecast effects of STAR-GARCH model, which makes the related theory of STAR-GARCH model to be more complete, and reasonably for explaining the macroeconomic and financial problems.In the theory aspect of the research, this paper’s main work and innovation are as follows:(1) This article summarizes the nonlinear form of setting and testing of the mean and variance equations under STAR-GARCH process; discusses the estimate of STAR-GARCH model, with the aid of the Monte Carlo simulation, the method verify parameter estimator of the consistency and asymptotic normality under the simultaneous estimate about STAR-GARCH model(2) Discussed the unit root test of mean equation under STAR-GARCH process derived the limit distribution of the test statistic for unit root test by using maximum likelihood estimation, and through the Monte Carlo simulation analysis the finite sample properties of the test statistics. Further, analyze the influence of the stationarity of the variance equation on the unit root test under STAR-GARCH process by using the Monte Carlo simulation.(3) On the basis of the real data generation process of the sequence follows the STAR-GARCH model, discuss the in-sample forecast and out-of-sample forecast, and combining the corresponding evaluation index and the Monte Carlo simulation method to analyze the forecast effect of the STAR-GARCH model, by comparing forecast effect under the model accurately setting and set by mistake, emphasizes the importance to avoid model overfitting and set by mistake from the angle of out-of-sample forecast.On the empirical research, this paper’s main work and innovation are as follows:(1) Based on the monthly data of inflation rate from January1990to December2012, describe the nonlinear dynamic characteristics of inflation in China. The research suggests, in the sample period, the nonlinear dynamic characteristics of inflation in China can be described by LSTAR-GARCH (1,1) model, conditional mean of inflation rate series show significant nonlinear smooth transition characteristics, while the conditional variances has the GARCH effect, show the rush thick tail phenomenon. At the same time, with the aid of the Monte Carlo simulation method, concretely forecast the monthly inflation rate by AR model, AR-ARCH (1) model, LSTAR model and LSTAR-GARCH(1,1) model from January to June,2013, the results show that the LSTAR-GARCH(1,1) model established by this paper has optimal in-sample forecast and out-of-sample forecast effects, the establishment of the model is suitable.(2) Establishes LSTAR-GARCH model to describe the real data generation process of Shanghai composite index and Shenzhen component index, on this basis, with the rolling analysis to conduct out-of-sample forecast by comparing the prediction effect under the real data generation process and the martingale hypothesis. The study found that after April29,2005, at the beginning of the share reform, Shanghai and Shenzhen stock markets are not weak form efficient market, after introducing stock index futures on April16,2010, Shenzhen stock market efficiency enhancement and work up to weak-form market efficiency, but Shanghai stock market has not yet reached the weak type of effective market. At the same time, evidence of economic sense also support this conclusion, after the introducing of Stock index futures, The Shenzhen component index’s arbitrage possibility is very small, but the Shanghai composite index still exist arbitrage space. The results show that the effectiveness of the stock market remains to be enhanced.