Taylor's Law of temporal fluctuation scaling in stock illiquidity

Qing Cai, Hai-Chuan Xu and Wei-Xing Zhou
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Qing Cai: ECUST
Hai-Chuan Xu: ECUST

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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.

Date: 2016-10
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Published in Fluctuation and Noise Letters 15 (4), 1650029 (2016)

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