Multiscale relationship analysis of power-law distribution and correlation in Chinese stock market

Studying on relationship of multiscale between power law distribution and correlation of the Shanghai Securities Exchange Compound Index (SSECI) through 5-min returns dataset, we find that accelerating decay of power-law distribution has little effect on the correlation properties of returns, but stabilizes correlation of absolute returns. Furthermore, we also analyze the impacts of short-range, nonlinear and nonlinear long-range correlation on power-law properties of returns by constructing three different types of shuffling series. The empirical results indicate that except for correlation, time scale may also be an important factor in maintaining power law property of returns. When time scale is less than the critical point, the effects of correlation are robust with nonlinear long-range correlation presenting the strongest influence. However, for time scale beyond the critical point, the impact of correlation begins to diminish or even finally to disappear, and then the power law property shows completely time scale dependent.