Empirical Study On Worldwide Main Stock Index Based On MRS-GARCH Family Models

Aimed at the Chinese multi-layer stock market,MRS-GARCH family models have beenestablished with the daily yields of Shanghai composite index、SME’s index、GEM’s index、HongKong’s Hang Seng index and S&P500index,which consist of GARCH model、EGARCH model、PARCH model、MRS-GARCH model.Furthermore，deep research has been undertaked about thecomparison between the Chinese mainland stock market and the developed stock market,just asthe Hong Kong stock market and the American stock market.The empirical analyses demonstrates that PARCH-t model do fit the Shanghai compositeindex,GARCH-t fits the SME’s index well,and as to the GEM’s index,it makes a difference that inview of the AIC criterion GARCH-t model outperforms the others,while PARCH-GED works wellaccording to the Loglikehood statistic.The results also reflect a truth:the GEM’s index has a highervolatility than other boards.At the same time, PARCH-t model fits S&P500index well,whenPARCH-GED model gets an outstanding performance at the Hang Seng index. MRS-GARCH-Nmodel fails mostly because of its normal innovations.Several analyses also have been taken on the great reform of the shareholder structure of listedcompanies.In view of both the presence of high volatility and the leverage effect，the Chinesemainland security market have advanced,obtained sustainable development,which is due to theundergoing reform.The last but not the least important, aimed at the heat topic that whether the excess volatilityexist,a new model has been established with the daily yields of Shanghai composite index、SME’sindex and S&P500indexes.The key point of the model is using the conditional standard deviationof stock indice’s yield rate,which could be generated by the standard GARCH models.Theempirical analyses demonstrate that excess volatility do exist in SME，compared to the Chinesemain borad,also draw the conclusions that excess volatility exists in Chinese securitymarket,compared to the USA security market.The most importance here is that these researchescarried are in mostly accord with the trend of stock indice,at the same time show the applicabilityand correctness of this model.