Basic On Fractal Theory For The Research And Quantitative Application Of China's Stock Market Characteristics

With the passage of time and the continuous research of many scholars,we find that more and more stock market visions and empirical research are contrary to the effective market hypothesis,while China's capital market is a nonlinear mixed system with many complex behaviors,using fractals.Linear theory can better describe the law of fluctuations in China's stock market.Based on the previous research results,this paper explores and studies the multi-fractal characteristics of the Chinese stock market represented by the Shanghai Composite Index.At the same time,this paper also uses the empirical results to construct a fractal quantitative investment strategy.According to the ideas from macro to micro,from single dimension to multiple dimensions,this paper uses Hurst exponent,wavelet analysis and multifractal spectroscopy to obtain single-fractal characteristics,macro-sequence multifractal characteristics and high-frequency data fluctuations characteristics respectively.The cyclical transition and continuation of the Shanghai Composite Index are accompanied by the occurrence of the minimum and maximum values of the Hurst index,indicating that the Hurst index confirms the long-term memory of the Shanghai Composite Index;The results of wavelet analysis show that the wavelet coefficients have regularity and singularity in the time and scale of the Shanghai Composite Index rather than evenly distributed.but in general,the Shanghai Composite Index has four main cycles with a period of six months,one year,two and a half years,three and a half years.On the other hand,the energy of the wavelet power spectrum is stronger at the time of the financial crisis.All these indicate that the Shanghai Composite Index is a complex multi-segment system.At the end of the empirical study,this paper uses multifractal spectrum to analyze the high-frequency data of the Shanghai Stock Exchange for 5 minutes,and finds that the evolution of multifractal spectrum before and after the fluctuation of the index price has a clear law.In the end,we use the two quantifiable indicators,Hurst index and multi-fractal spectrum parameters,to construct a quantitative investment strategy.The Hurst index strategy is superior to the non-strategic market gain in winning ratio,average return rateand cumulative return rate.However,the cumulative rate of return in the bull market has lagged behind the market's earnings.In comparison,the multifractal spectrum strategy has achieved good returns.Whether it is winning ratio,average return rate and cumulative return rate,it has always led the market and achieved excess returns,which has certain practicability and reliability.The article concludes that the trading time points based on the multifractal spectrum strategy are very effective,which also verifies that the conclusions of using the multifractal spectrum to study the law before and after the stock price fluctuation are correct.