Arch Models In The Application Of Comparative Analysis

The Autoregressive Conditional Heteroskedastic(ARCH) class of models for conditional variances was put forward by Engle(1982) proved to be extremely useful for analyzing economic time series. GARCH models have been developed to account for empirical regularities in financial data. Many financial time series have a number of characteristics in common. Firstly, the logarithmic return series usually show no or little autocorrelation, whereas the squared values or absolute values of the series have high autocorrelation. Volatility of the return series appears to be clustered. Secondly, normality has to be rejected frequently in favor of some thick-tailed distributions. Thirdly, some series exhibit so-called leverage effects, that is, changes in stock prices tend to negatively correlated with changes in volatility.The normal,srudent's t and stable Paretian distributions with their characteristics are firstly introduced. Research indicates that student's t and stable Paretain distributions have the characteristics of leptokurtosis. Secondly, GARCH and EGARCH class of models for financial time series are introduced. It is proved that GARCH(1,1) with student's t innovation is more of leptokurtosis than GARCH(1,1) with normal innovation. The use of GARCH models with stable Paretian innovations in financial modelling has been recently suggested in the literature. The extension of EGARCH model with stable Paretian distribution and a sufficient condition for the stationarity are put forward. Subsequently, the methods of goodness-of-fit test of distribution and model are introduced. It is found from the comparison of PP plot and QQ plot that PP plot is a more interpretable graphical goodness-of-fit test. In the application of PP plots, unconditional variance distribution of logarithmic return and ARCH type models are tested.In the empirical analysis, PP Plot or other test methods show that logarithmic return time series of financial assets have leptokurtosis and heteroskedasticity. It is found from the comparison that the ARCH type models with stable Paretian innovation is more capable to capture characteristics of financial time series than ARCH type models with normal and student's t innovations. Specially,ARCH type models with stable Paretian innovations can better asset risk in terms of calculating VaR of financial logarithmic return. The comparison of VaR of stock indices indicates that the risk of Shanghai stock market and Shenzhen stock market are larger than Hong Kong stock market and American stock market. In the end, this paper examine the forecasting performance of ARCH type models for the weekly Shenzhen stock market volatility. The results suggest that ARCH type processes driven by stable distribution is more effective than the others.