Analysis Of Stock Index Time Series Based On Fractal Theory

We analyze and research Chinese stock markets by using fractal theory in thisthesis. Firstly, the law of change and the structure character of stock index time seriesare investigated by fractal interpolation models and the R/S analysis. We study thelaw of change of the Shanghai Composite Index during a certain time by establishingfractal interpolation models, and predict the tendency of change of the index in theshort term. Using the R/S analysis and Hurst index, we analyze the structure characterof the Shanghai Composite Index, and point out that the market has the persistence ofstate and the statistical properties of fractal distribution. Secordly, taking5minuteshigh frequency data time series of Shanghai Composite Index and ShenzhenComponent Index as research objects, we study empirically the multifractality of thetwo index time series by making use of multifractal spectrum, and compare theirfractal structure character and depict their multifractality. Further, we divide stockindex time series into two or more sections, and study multifractality of different partsand the relationship of parameters of multifractal spectrum between the different partsand the whole time series. Finally, we compare the multifractality of Shanghai andShenzhen stock markets based on different time scales. Our researches present thefollowing results:1. A new method is proposed for the computation of vertical scaling factors ofiterated function system, and a model of fractal interpolation is established, which canbe used for the analysis and prediction of the change of stock market index. Theresults show that the simulation and prediction of stock index based on fractalinterpolation theory are feasible, and the results of simulation and prediction areconsistent with the reality.2. We analyse the structure character of Shanghai Composite Index by using R/Smethed and Hurst exponent. The results obtained show that Shanghai CompositeIndex has the long-range dependency and the structure character of fractal statistics.We also find that Shanghai stock market has a non-circular peried of180-day byusing V statistics.3. We confirm that Shanghai and Shenzhen stock markets have multifractality bymeans of studying multifractal spectrums of the5minutes high frequency data timeseries of the two stock indice. Shenzhen stock market has stronger multifractality thanShanghai does. 4. Using segmental analysis for the Shanghai and Shenzhen stock index timeseries, we find that multifractality of high frequency data time series increases inevery segment, and the corresponding order of partition function also increases, aswell as the percentage of the number of stock index located in the peak and valleyalso grows.