Taylor's Law of temporal fluctuation scaling in stock illiquidity

Abstract

Taylor's law of temporal fluctuation scaling, variance \(\sim\) \(a(\)mean\()^b\), is ubiquitous in natural and social sciences. We report for the first time convincing evidence of a solid temporal fluctuation scaling law in stock illiquidity by investigating the mean-variance relationship of the high-frequency illiquidity of almost all stocks traded on the Shanghai Stock Exchange (SHSE) and the Shenzhen Stock Exchange (SZSE) during the period from 1999 to 2011. Taylor's law holds for A-share markets (SZSE Main Board, SZSE Small & Mediate Enterprise Board, SZSE Second Board, and SHSE Main Board) and B-share markets (SZSE B-share and SHSE B-share). We find that the scaling exponent \(b\) is greater than 2 for the A-share markets and less than 2 for the B-share markets. We further unveil that Taylor's law holds for stocks in 17 industry categories, in 28 industrial sectors and in 31 provinces and direct-controlled municipalities with the majority of scaling exponents \(b\in(2,3)\). We also investigate the \(\Delta{t}\)-min illiquidity and find that the scaling exponent \(b(\Delta{t})\) increases logarithmically for small \(\Delta{t}\) values and decreases fast to a stable level.