Tail Index Estimation Of Heavy-tailed Distribution And Empirical Analysis Of China's Stock Markets

The heavy tail characteristic of distributions exists generally in many fields, such as marginal distributions of the economy finances,traffic,hydrology and meteorology domain and so on, high frequency time series almost all are the heavy tail. Therefore, wanting to obtain the anticipated extreme event to occur probability must be able to describe the distributed heavy tail degree correctly. So, how to estimate effectively tail index of the heavy tailed distributions,which is always focused by statisticians..In this thesis, we elaborate systematically the extreme value theory and the heavy tail distribution, and review estimating tail index of the heavy tailed distribution historic course .We summarize selecting k from the heavy tailed distribution index to the research state, discusse the heavy tail index to estimate in detail selecting kthe Sum-plot method and Bootstrap method, and further improves the Bootstrap method which proposed by Hall, so made called the M-Bootstrap method. And we use the above three methods to carry on the Monte-Carlo simulation to the known heavy tail distribution, studies their feasibility , compares with their robust. Afterwards we make empirical analysis basing on Shanghai and Shenzhen's stock index data, the computed result indicated that Shanghai and Shenzhen stock index returns ratio is of thick tail and expose right skewness, right tail heavier on left tail. At the same time, we discuss the anomalous value impact on tail index estimate of the heavy tailed distributions. Finally, we further discuss the tail index estimation basing on the GARCH model. The empirical results indicated that time series supposed by us following the model has the very tremendous influence on tail index estimate of the heavy tailed distributions. The index estimation value of the heavy tailed distributions basing on the GARCH-t model is larger.Main conclusion of this paper as follows:Overall, we can obtain the satisfying results by using the Sum-plot method and the Bootstrap method. The Sum-plot method surpasses the Bootstrap method and the M-Bootstrap method. The Sum-plot method and the M-Bootstrap method precise in estimating heavy-tailed index and is immune to anomalous value.The China Stock market's index returns ratio obey heavy tailed distribution .It presents right skewness, their tail index is around 3. GARCH-t models can reflect well the stock market undulation continues Under t distribution supposition, GARCH model can reflect returns ratio accurately especially . ARCH -type dependence sit- uation effect on the tailed index estimation of marginal distribution. The tail index value basing on GARCH(1,1)-t model is larger than the tail index estimation value which is free of condition supposition.