Research On The Dynamic Characteristics Of Skewness Kurtosis Of The Stock Market

Traditional risk analysis based on mean-variance ignored the third moments risk and the fourth moments risk. As a result, it underestimated the risks. At the same time, the traditional assumption of normal distribution constantly suffered from shock in financial practice. Economists began to focus on the non-normal distribution of financial assets, that is, financial assets have the problems of negative skewness and fat tail.Traditional GARCH models included the time-varying characteristics of the variance, but did not consider time-varying characteristics of skewness and kurtosis. Then, models, such as GARCHS, GARCHSK, NAGARCHSK etc, began to focus on time-varying characteristics of skewness and kurtosis, and then build models based on them.The purpose of the article is to study the dynamic characteristics of higher moments of stock returns of Chinese stock market in general and different sectors. The article selects six indices, including Shanghai Stock Exchange Composite Index, the Shenzhen Stock Exchange Composite Index, Industrial Index, Business Index, Real Estate Index and Utilities Index from January2005to June2013. The index capacity is2057for all the six indices.First of all, we analyze the basic statistical characteristics and the characteristics of time series of the six indices. We found six exponential logarithmic distribution yields a non-normal distribution, and exists the problems of negative skewness and extreme kurtosis. At the same time, six time series are stationary, and volatility, skewness, kurtosis has significant autocorrelation characteristics. Also, there exists autoregressive conditional heteroskedasticity phenomenon. Therefore, GARCH class model is suitable for the six indices.We discard the traditional assumption of normal distribution of GARCH model, and characterize the time-varying characteristics of skewness and kurtosis using the assumption that the residuals obey the dynamics of the skewed-t distribution. Compared to traditional t-distribution, dynamics of skewed-t distribution contains the asymmetry parameter. Compared to static skewed-t distribution, the dynamic of skewed-t distribution breaks through the limitation of the static freedom and the static asymmetry parameter. In this article, we use the ARMA(1,1)-GJR(1,1) model with residuals obeying the dynamics of the skewed-t distribution. This model can be used to describe the characteristic of negative skewness and extreme kurtosis.Then, we use the results from ARMA(1,1)-GJR(1,1) model with residuals obeying the dynamics of the skewed-t distribution to analyze the factors that impact skewness and kurtosis. Also, we briefly analyze the mechanism of skewness and kurtosis.Through the above analysis, the main conclusions drawn in the article are:Firstly, there exists significant risk of third-moments and fourth-moments risk in the Chinese stock market. Variance, skewness and kurtosis of six indices have significant characteristics of time-varying. Secondly, by comparing the model, we find that t the ARMA(1,1)-GJR(1,1) model with residuals obeying the dynamics of the Skewed-t distribution fit better tha n the other four for dynamic modeling features of higher-order moments. Thirdly, on the whole, lags yield, volatility, skewness and trading volume have some explanatory power on the skewness. And "bad information revealed" effect can explain the skewness in China’s stock market. Also, there is a significant stock market volatility feedback mechanism in China. Fourthly, except Real Estate Indices, the lags yield, volatility, skewness and kurtosis almost have no explanatory power on kurtosis.