The Application Of GARCH Model In China 's Stock Market

Statistical diagnosis plays an important role in data analysis. Its main purpose isto test the rationality of the established model fitting the observed data by using thediagnosis statistic. From a general perspective, time series is a list of the observeddata in time order. And it is a discrete random process from the point of view ofprobability. With the research on time series data extending and deepening constantly,applied, It has been formed a relatively mature theory in parameter estimation andprediction of time series analysis, and there is a certain degree of research in a modelwith dependency error term of time series statistical diagnosis. However, because ofthe existing of certain related structures of the time sequence model between the datapoints, the diagnosis of abnormal point and the strong impact point in time sequencemodel is relatively complex. Stock price index is a typical time series data, and stockprice index is the barometer to measure economic development of a country or region.In this paper we use stepwise local influence method proposed by Shi and Huang(2011) to detect patch of outliers in GARCH model in Chinese stock market. Wechoose three representative index as our research object. They are ShanghaiComposite Index, Shenzhen Composite Index, and the Growth Enterprise MarketIndex. Research on stock market volatility is mainly to study the risk, and yield canreflect risk better than prices. So we make first order difference to closing price aftertaking logarithm study again after processing. First we disturb all of the observationpoints and we can identify some strong influence points. Secondly, we put the stronginfluence points identified by the first step out of the set and then disturb the restpoints. After these two steps, the strong influence points have not been identified bythe first step will be identified in the second step. Process will be repeated until nonew impact point was found. Then the detection process is over.At the beginning, weuse local influence analysis to compare the performance of three differentperturbation scheme including innovative perturbation scheme, additive perturbationscheme and data perturbation scheme. The result shows that the innovative perturbation scheme give better result than other two schemes although thisperturbation scheme may suffer from masking effects. Secondly, to detect patch ofoutliers and uncover the masking effects, we use stepwise local influence methodunder innovative perturbation scheme. The results show that this method can detectall of the outliers successfully under innovative perturbation scheme. The analysisbased on three representative index data of the Chinese securities market show thatthe stepwise local influence method under innovative perturbation scheme is efficientfor detecting multiple outliers and dealing with masking effects in GARCH model.Besides, we choose the mean which plus or minus two standard deviations of thesample points in six groups of experiments as the initial judgment of abnormal pointstandard, and the outliers roughly detected by the method can also be detected bystepwise local influence method. It proves that sample points mean which plus orminus two standard deviations can be used as the basis of various identificationmethods to identify outliers. We also compare Shanghai Composite Index, ShenzhenComposite Index, and the Growth Enterprise Market Index. We find that the ShanghaiComposite Index has less outliers, and outliers are far far normal points.The resultsshow that the Shanghai Composite Index is less impacted by the external reaction. Itmeans Shanghai Composite Index is more stable.