Taylor's Law of temporal fluctuation scaling in stock illiquidity

TL;DR

This study provides the first evidence of Taylor's law in stock illiquidity, showing a consistent mean-variance relationship across various markets, sectors, and regions, with the scaling exponent varying systematically.

Contribution

It demonstrates the existence of Taylor's law in stock illiquidity data across multiple markets and regions, revealing systematic differences in the scaling exponent.

Findings

Taylor's law holds for most stock markets studied.

Scaling exponent differs between A-share and B-share markets.

Exponent varies across industries and regions.

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.