Multi‐scale relation analysis of power law distribution and correlation in the Chinese stock market

Abstract

PurposeThe purpose of this paper is to reveal the multi‐scale relation between power law distribution and correlation of stock returns and to figure out the determinants underlying capital markets.Design/methodology/approachThe multi‐scale relation between power law distribution and correlation is investigated by comparing the original series with the special series. The eliminating intraday trend series approach developed by Liuet al.is utilized to analyze the effects of power law decay change on correlation properties, and shuffling series originated by Viswanathanet al.for the impacts of special type of correlation on power‐law distribution.FindingsIt is found that the accelerating decay of power law has an insignificant effect on correlation properties of returns and the empirical results indicate that time scale may also be an important factor maintaining power law property of returns besides correlation. When time scale is under critical point, the effects of correlation are crucial, and the correlation of nonlinear long‐range presents the strongest influence. However, for time scale beyond critical point, the impact of correlation begins to diminish or even finally disappear and then the power law property shows complete dependence on time scale.Research limitations/implicationsThe 5‐min high frequency data of the Shanghai market as the empirical benchmark is insufficient to depict the relation over the entire time scale in the Chinese stock market.Practical implicationsThe paper identifies the determinants of market dynamics to apply them to risk management through analysis of multi‐scale relations, and supports endeavors to introduce time parameter into further risk measures and control.Originality/valueThe paper provides the empirical evidence that time scale is one of the key determinants of market dynamics by analyzing the multi‐scale relation between power law distribution and correlation.