The Analysis Of Stock Market Based On Fractal Theory And R/S Method

This paper gives specialized research to the features and regular pattern of 30 different stocks from Shanghai and Shenzhen stock market, and studys their inner characteristics in many aspects to acquire more and further recognition on the trend of stock share series, which enables the investors to gain more theory basis when they buy some stock and estimate its risk. This paper is expanded into three main parts to study and analyze the stock time series.1) Through the normality tests, All the sample stock-data curves show different phenomenon of Aiguille and Fat-tail, as well as Left-Deviation, which proves that none of the sample series belong to normal distribution, in other words, the linear method can't be applied into the analysis process, so we adopted the R/S method instead.2) The application of R/S method has verified the long-term memory characteristics of the sample series, and Support Vector Regression (SVR) is combined to enhance the precision of Average circle period.Meanwhile, we mainly introduce the SVR method. It appears as a new data-mining method to take place in the traditional regression method, which can also well solve the non-linear regression problem. Through the combination of SVR method, R/S log-log type curve and V-statistics curve, Average circle period is tested, which not only maintains its own original trend of the curves, but also becomes smoother. The integrated method has greatly boosted the precision of the average circle period in the stock time series.3) We expect to find the rules of the stock time series by using rough sets, this process includes two parts, data Pretreatment and F-rule discovery.Data Pretreatment part needs to clean the stock time series data first, and then divide them into different time intervals according to their respective transformation tendency. Ensure that the trend in every time interval keeps single and changeless, thus all the time series are transformed to a series of totally static pattern, and every pattern represents a behavior trend and their time dependence can be ignored. The respective attribute of every pattern is extracted to build an information table which can be processed by the rough sets theory. Finally, we operate the information table through rough sets theory to find the F-rule.Result Analysis: The selected 30 stocks from Shanghai and Shenzhen stock markets generally have the fractal feature, their transformation courses are circulatory. When the discovered rule of stock risk is larger than its original rule, its related stock Hurst index is usually lower than 0.59, indicates that once a stock's Hurst index is below 0.59, its stability is relatively weak, especially when encountering the invading of risk attributes, the possibility of appearing reverse fluctuation for the stock will be bigger in the following trend.