Taylor’s Law of Temporal Fluctuation Scaling in Stock Illiquidity

Abstract

Taylor’s law of temporal fluctuation scaling, variance [Formula: see text], 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 [Formula: see text] 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 [Formula: see text]. We also investigate the [Formula: see text]-min illiquidity and find that the scaling exponent [Formula: see text] increases logarithmically for small [Formula: see text] values and decreases fast to a stable level.