The Research Of Fractal Characteristics Of China’ Stock Market And Its Applications

Price behavior of the stock market has been characterized by research academics and investment practitioners in the hot issues of wide concern. Random Walk and effectiveness of market prices is an important cornerstone of the mainstream financial measure theory theory. However, with the development of the market, efficient market theory mainstream constantly under actual operating conditions test the market and related research. Financial research in physics fractal theory of financial markets more appropriate as a research tool to compensate for the lack of efficient market theory a large extent. So this paper, the fractal theory, the market features the Shanghai Composite Index and Shenzhen Component Index of16December1996to31December2013were studied, from the market’s overall multi-fractal characteristics of single fractal characteristics and market structure to comprehensive understanding of the market.Characteristics of single fractal shows that the Chinese stock market:the stock market is a nonlinear system. Share price movement does not meet the Brownian motion and geometric Brownian motion, comparatively speaking, fractional Brownian motion is a better description of volatility. Meanwhile distribution yield, not a good description can be normal, and the fractal has a fat tail of the distribution, but can be used to describe the distribution of returns. This shows the fractal market to understand the stock market more in line with the actual situation. Overall, the Chinese stock market has statistical self-similarity, price trends under different time scales have similar morphology, yield under different time scales have a similar distribution. Meanwhile, R/S analysis shows that the Chinese stock market is a non-efficient market, the market has a long memory characteristics, price volatility and the historical volatility of information will affect the future of the past, so the price is to some extent predictable. A further period of long memory measure showed that, on average, the Shanghai index’s long memory will be reduced in30days,70days will disappear, long memory Shenzhengchengzhi will decrease in30days,60days will be disappear. Single fractal characteristics indicate the overall characteristics of the market, further use of multi-fractal theory of structural features of the market research showed that:China’s stock market there are multi-fractal structure, between the large minor fluctuations in share price returns, as well as low priced stock price distribution of between different fractal. In terms of yield, based on the generalized Hurst exponent Research MF-DFA method measured show that China’s stock market volatility has anti-persistence characteristic, slight fluctuations persistent feature, which shows that when market volatility occurs when there is a large probability will change the original price trends, and slight fluctuations occur when there is a greater probability that the trend to maintain the original run. In terms of the stock distribution, Holder index, spectral function through the use of multi-fractal spectrum of research, found that China shares at a higher price and lower in different price level of the singularity in the sample time, and come to the difference between this singularity the overall price volatility, and when the overall volatility of the share price, the gap between high and low-priced singularity greater; Meanwhile, studies show that the spectral function in the sample time China shares distributed in low-cost high probability, which is China stock market experienced a peak in2007after a prolonged slump in the real portrayal.China’s stock market single fractal and multi-fractal characteristics suggest that the stock market is a complex, chaotic system, seemingly disorderly orderly market, but there are features, price changes in the market there is a pattern. Thus, theoretically, the stock to some extent can be predicted. So in practice, how to find useful information in favor of financial investments based on fractal characteristics of China’s stock market, the paper did research on this.The fractal characteristics of single market and financial investment by combining features of the market according to mutation long memory, the paper calculated the short-term and long-term moving mobile Hurst exponent Hurst exponent law of motion, you can find useful information indicative of future price movements. This investment in the stock market has important practical significance. On the other hand, the multi-fractal characteristics combine with financial investment market, through the study of high-frequency data found that the method based on multifractal spectrum measure market Holder index can be used as a measure of the difference△α day price volatility indicators; while the difference△f spectral function can be used as the direction of the day the stock distribution, the distribution ratio of index cases. This financial investment process, particularly quantitative investment, the quantification of the market characteristics provide a powerful reference tool. Further, the Chinese stock market single fractal, multi-fractal characteristics combined with fractal characteristics of quantitative indicators as input information, the use of neural network model to scroll to simulate the stock market short-term trend, discovered can get a better prediction, which for the stock market price forecasting has practical significance.