Research On The Stock Markets Index Based On Return Interval Approach

With the developing of China’s financial reform,the stock market has become anindispensable part of the security and financial market, several scholars put forward theresearches of stock market rules in various ways.In this paper, by the distribution of riskreturn interval and method of complex network,the Shanghai Composite Index has beenanalyzed about the relation between average time of return interval and the threshold valueand the network characteristics of return interval sequence.Then the return intervaldistribution of Bear Market and Bull Market period of Shanghai Composite Index hasbeen contrasted and extracted, and define the index of financial market prosperity.Themethod then has been applied to comparison of Growth Enterprises Market Index andShanghai Composite Index, classification of the market index of29industry group whichenhance the understanding of the stock market fluctuation.In the paper, the daily value of Shanghai Composite Index and other indexes havebeen changed into the sequence of risk (exceed a certain threshold of the absolute value oflog-return) return interval and get a unified distribution on different thresholds by ascaling law.There are two properties of the Shanghai Composite Index: a linearrelationship between threshold value and average return interval;in the sequence, the shortinterval transform with each other frequently and the long interval could only transformwith each other via the short interval.Then extracting the return interval characteristics by the comparison of the Bear andBull Market periods and defining the prosperity index and applying the method tocomparison of Growth Enterprises Market Index and classification of the market index of29industry group,and getting the following conclusions:(1) The higher probability of scaled short-interval,the more prosperous of thefinancial market of the great Bull Market,the small Bull Market,the turmoil and the Bear Market periods of Shanghai Composite Index which could be applied to classify theprosperity of the financial market by ration of scaled short-interval and scaledmedian-interval;(2) Compared with the Shanghai Composite Index,the Growth Enterprises MarketIndex has higher probability on scaled short-interval and higher fluctuating frequency;(3) There are three groups of industry index which have the same kind of distributionof the Shanghai Composite Index based on the prosperity and two groups according tothe different degree of the Shanghai Composite Index distribution that refine the degree ofmarketization and the development of different industries in Chinese stock market.