Fractal Character Analysis Of Stock Market Returns In China

Fractals as a new nonlinear science was developed in the1970s, its researchobjects are those irregular objects and phenomena in the nature, which have somecharacteristics of self-similarity. Fractal theory provide us a new perspectives andmethod ology to view the world. Recently, with the appearance of the complicatedcharacter of stock market, the traditional linear thinking cannot adapt to the realeconomic system, more and more scholars use fractal theory as a nonlinear tool toresearch the complex behavioral of financial market.In this dissertation，chapter one gives some preliminaries. First, the developmentbackground of fractals and review of research on applications of fractal theory in thefinancial markets are introduced briefly. Then we show that the reality of capitalmarket is a nonlinear fractal market. The application of fractal analysis method infinancial markets, and the review of the research works which have already achievedby domestic and foreign researchers are explained. In chapter two, we study fractalcharacteristics of stock market in China. The method of rescaled range analysis isused to study the fractal characteristics of Shanghai composite index and Hushen300index. Taking time series of daily and monthly return rates and four price sequencesof stocks as research objects, we investigate the Hurst indexes, lengths of averagecycle, relevant indicators and fractal dimensions of these sequences. The positiveanalysis shows that the two stock markets have the obvious fractal structurecharacteristics, and also have the sustainability of state, the periodicity of prices.Under the certain time scales, Hurst index has increasing trends when the time scaleincreases, and the fractal dimensions of four price sequences of stocks areapproximately equal. Since unifractal analysis only can exhibit the macroscopiccharacter of objects, the internal economic structure information of the objects cannotbe described in detail. Multifractal analysis can explore different fractal characteristicsof every point of the objects. The methods of multifractal detrended fluctuationanalysis and multifractal spectrum analysis are used to study the structurecharacteristics of stocks of the Wanke and Baoli real estate companies, which arelisted in Shenzhen and Shanghai stock markets respectively, in the chaper three.Taking the time series of the logarithmic return rates of every5min opening pricedaily as research objects, some basic statistical parameters show that the twodistributions of return rates have the feartures of steep peak and long tail. By taking different orders of fluctuation, we note that the generalized Hurst exponent decreasesas the orders increases, and quality index increases as the orders increases. Usingmultifractal spectrum function and singular standard scale index, we depict the fractalfeatures of the sequence of return rates and analyze the relevant results. The empiricalanalysis shows that the two sequences are non-normal distribution, and havemultifractal characteristics. Compared with their multifractal nature and some relatedfractal features, we find that the sequence of the stock return rates of Baoli real estatecompany has more stronger multifractal characteristics than those of Wanke group,and hence the risks of the stock of Baoli company are relatively greater. Chapter fourmakes a summary for this thesis and prospects the future development of fractals.