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Research On Multifractal Theory And Its Application In Stock Markets Of China

Posted on:2008-10-07Degree:DoctorType:Dissertation
Country:ChinaCandidate:B YuanFull Text:PDF
GTID:1119360308479929Subject:Management Science and Engineering
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Stock price fluctuation in stock markets is a very important issue in financial researches. The right description to the evolution law of stock markets and to the running mechanism of stock prices is related to assets pricing,risk controlling,markets supervision and price prediction. After systemically analyzed the multifractal theory and deepened the methods of it, an empirical research on the stock markets in China is presented. The main research work of this paper is as follows:1. The abnormal characteristics of stock markets in ChinaThrough studying the basic statistics,long-term memory,clustering property,multi-scaling property of the stock price index returns and predictability of stock price index, some conclusions can be drawn:(1) The returns series of Shanghai and Shenzhen stock markets are disobedient normally distribution but has obvious peak kurtosis and fat tails; And the returns series of Shanghai stock market has peaker kurtosis and fatter tail than those of Shenzhen stock market.(2) The stock markets of China are not efficient markets, and the returns series had obvious long-term memory, indicating that the stock market did not reached the soft efficiency.(3) The clustering structure and multi-scaling behavior of the time series were revealed. It indicates that a single scale exponent is insufficient to describe the scaling properties of the returns series and a multifractal model may be more suitable for describing the time series.(4) The variation of the stock price in China is not totally random, but predictable, or at least predictable in a short period of time.2. The multifractal characteristics of stock markets in ChinaUsing MF-DFA,multi-affine,qth-order moment structure partition function and a quadratic function fitting to study the returns series and the stock price index series in China, some conclusions can be drawn:(1) The returns series of stock markets in China showed pronounced multifractal characteristics. Furthermore, the sources of multifractality are analyzed. It is found that there are two different types of sources for multifractality in time series, namely, fat-tailed probability distributions and nonlinear temporal correlations. Most multifractality of the series is due to different long-term correlations, but the fat-tailed probability distributions also contribute to the multifractal behavior of the time series.(2) The returns series showed a crossover time scale. This crossover divides the whole time scale into two different scale domains. There are different multifractal characteristics and scale exponents for these two different domains. The strength of multifractality in time scales ss*.(3)The stock markets showed multi-affine phenomenon. In addition, it is found that the generalized Hurst exponents H(1) and H(2) show remarkable differences between developed and emerging markets:Emerging markets are associated with high value of H(1) and developed markets are associated with low values of H(1). Besides, it is found that all the emerging markets have H(2)>0.5 whereas all the developed have H(2)≤0.5. The stock markets in China belong to the category of emerging financial markets.(4) There are pronounced statistical correlations between the parameters of the multifractal spectra and the variation of the closing index, the logarithmic return and the gain probability. And when the stock price index fluctuates sharply, a strong variability is clearly characterized by the multifractal parameters (α0,αmax,αmin, W and C).4. Forecasting research of stock price in ChinaThrough directional prediction and nonlinear prediction to the stock price in China, some conclusions can be drawn:(1) Both of two sign sequence methods have the forecasting capacity. One is the symbol sequence of difference of daily closing quotation indexes; the other is the symbol sequence of multifractal spectrum parameter of the high frequency data. The relation between the condition of different symbol sequences and changes of index in larger fluctuating of stock price index is stronger than the relation in smaller fluctuating of stock price index when threshold values are introduced. And the combining of these two methods has remarkable forecasting capacity.(2) A neural network model based on the multifractal spectrum is advanced and is applied to the stock price forecasting. The test results indicated that the model can simulate stock market trends in a short time. It is useful to prevent and control risks.
Keywords/Search Tags:multifractal, long-term memory, neural network, multi-affine, multifractal detrended fluctuation analysis, forecasting
PDF Full Text Request
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