Comparative Research on the Industry Indices of Chinese Stock Market Based on Multifractal and Neural Network

In this paper, the multifractal degrees in a collection of Chinese market and industry indices are evaluated. Via the multifractal detrended fluctuation analysis (MF-DFA), the result shows that all the indices have the multifractal features, but their multifractal spectrums differ from each other. The average fractal dimension is also calculated and applied to measure the market risk. According to the chaotic characteristics of the stock market, the correlation dimension and the smallest embedding dimension of the market index are calculated by phase space reconstruction. At last, based on the multifractal and chaos analysis of the financial market above, all the indices are compared and categorized by the self-organizing feature map neural network (SOM). It is found that the neural network combined with chaos and fractal can distinguish well the indices, which provides a new way to optimize the portfolio and manage the financial risk.