Multifractal Identification And Application Research Of China Stock Market Based On The Wavelet Analysis

This dissertation explores and studies the fractal and multifractal theory, as well as their application in Chinese stock market price series identification and prediction, and obtained the following results:1. Study the fractal and multifractal theory. Introduces the fractal theory and the fractal of the basic concept and the characteristic, Introduces several features of the fractal time series, finally expounded the multifractal theory and the multifractal process of the time series. Defines the local Holder index and multifractal spectrum of the time sequence. And put forward the multifractal spectrum method of calculation the time series of China stock market price.2. Study the method of eliminating noise jamming of Chinese stock price time series.Introduced some basic concepts of the wavelet theory and used multiresolution analysis method of wavelet theory on Chinese stock market's (Shanghai Composite Index, the Shenzhen stock exchange and the Hang Seng index)day closing price indices for eliminating noise jamming. Combined with wavelet theory and fractal theory is proposed for the method of identification the multifratal feature of Chinese stock market.3. Get the method of calculating time series multifractal spectrum—wavelet transform modulus maxima (WTMM) method. And with the method the multifractal spectrum of Devi curve is calculated, the calculated values agree well with the theoretical value, and not subject to the effects of parameter setting. The day closing price time series of Shanghai Composite Index, the Shenzhen stock exchange and the Hang Seng index which is removed their noise interference were identificated their multifractal characteristics. The results show that the stock market in China after removing noise has more obvious multifractal characteristics.4. Forecast Chinese stock market which existed multiple fractal characteristics, if using traditional methods for modeling predictions is clearly not good effect. This dissertation try to use wavelet neural network to model for forecasting, the empirical results show that the prediction result is ideal, in particular the Shanghai index get a good effect of forecast, not only the predict of the market trend is in striking agree with the actual situation, and the predict of the price index is not error to the actual value. The forecast of the Shenzhen index and the Hang Seng index still exists some errors, but the prediction of trend consistent with reality, so judge the market prices have certain guiding effect.Finally summed up the research work and the main conclusion, points out the problems that need to further improve and in-depth study.