The Study Of Probability Distribution And Time Correlation Of High Frequency Ensemble Data Of Chinese Stock Market

We study the probability distribution, long memory and multi-fracial properties of two important variables, which are the ensemble return and the ensemble volatility of one minute stock close price, using the high-frequency data of all the A stocks'one minute close price from 2000.01.01 to 2008.03.31 in Shanghai stock market. We find that the probability distribution of one minute ensemble return meet the Student's distribution, with its characteristic exponentζ= 3.1538, obeying the inverse cubic law. And we also find that one minute ensemble volatility has intraday effect with "L" shape intraday pattern, its probability distribution and complementary probability distribution are both meet the power-law distribution, but their exponents don't obey the inverse cubic law. We study the long memory of one minute ensemble return using Detrended fluctuation analysis method with the result show that its Hurst index close to 0.5, which indicate that one minute ensemble return follow random work, and doesn't have long memory. On the other hand, the Hurst index of one minute ensemble volatility is close to 1, which indicates one minute ensemble volatility has long memory. We respectively study the multiracial characterize of one minute ensemble return and its volatility with Multiracial detrended fluctuation analysis method and Box-counting method, and find that the multiracial scaling exponentτ(q) of one minute ensemble return is a nonlinear function, the singularity strength exponentαdoesn't equal to 1, and△αis much larger than 0, which indicate that one minute ensemble return has multiracial characterize; otherwise, the multiracial scaling exponentτ(q) of one minute ensemble volatility is a linear function, its singularity strength exponent a is close to 1, and△αis close to 0, which indicate that one minute ensemble return doesn't have multiracial characterize.