The Research On Nonlinear Multifractal Behaviors In Chinese Security Market

Efficient Market Hypothesis (Efficient Market Hypothesis, EMH) is the bases for modern finance theory, the main idea of EMH is that the market prices reflects all information of market, volatility of market price are independent and unpredictable, the return series obey the random walk Hypothesis, and the distributions of it is normal or logarithm normal distribution. But the abnormal financial vision means that the traditional financial theory exist great limitations, it shows that the capital market is not a linear system, but a nonlinear system. For this we have to understand the basic rules of the capital market with nonlinear fractal theory.The basic view of nonlinear fractal theory is that the capital markets has fat tail characteristics, market volatility show multiple fractal features. The return series have some persistence and antipersistence character,and different voltility show the character of multifractal character.so the fractal theory can reveal the volatility essence more accurately than that of traditional capital market theory, and reveal basic law in finance market more efficiently also.With fractal theory and multifractal theory.This paper focuses on the research of Chinese growth enterprize market, the main contends as follows:(1) Chinese growth ernterprize market (GEM) is analysised with multiple fractal approach, detect the multifractal character in GEM index, GEM industry index and individual listed company in GEM is detected.(2) Taking the fitting function in multifractal model to deal with China’s growth enterprise market, and statistical results are more universality.(3) The study of multifractal character for return sequence in GEM in china with the moving time window method is given, not only reveal the volatility trend of GEM from macroscopic views, but also from the microscopic views reveal the multifractal characters, and this provide empirical basis for exploring the capital market law(4) Multifractal feature of Chinese GEM is analysised with random and phase random thoughts,and multifractal reasons are points out. (5) The corrolation amony Gem index, Gem industry index, and Gem company with multifactal detrended corrolation coupled analysis is revealed.(6) A new portfolio theory based on multifractal detrended method was put forward, and the empirical adjusted returns got is better than that got with the China securities investment fund portfolio strategy.