Taylor’s Law of Temporal Fluctuation Scaling in Stock Illiquidity

Abstract

Taylor's law of temporal fluctuation scaling, variance ∼ 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 ∈ (2, 3). We also investigate the ∆t-min illiquidity and find that the scaling exponent b(∆t) increases logarithmically for small ∆t values and decreases fast to a stable level.

Cross-sectional fluctuation scaling in the high-frequency illiquidity of Chinese stocks

“…Taylor's law can further be extended to higher orders using the k-th vs. the j-th cumulants [35], where the special case of k = 2 and j = 1 recovers the convention expression of Taylor's law. In addition, there is evidence showing that stock illiquidity, a nonadditive quantity, also complies with Taylor's law of temporal fluctuation scaling [36]. Here, we investigate the high-frequency illiquidity time series of Chinese stocks and confirm the presence of Taylor's Law of ensemble fluctuation scaling in stock illiquidity.…”

“…We further observed that Taylor's scaling exponents of stock illiquidity are not related to the ensemble mean and ensemble variety of stock returns. Our analysis unveiled a new scaling law of financial illiquidity that complements Taylor's temporal fluctuation scaling law of illiquidity [36].…”

Analyzing and interpreting spatial and temporal variability of the United States county population distributions using Taylor's law

“…Most but not all empirical estimates of TL's slope fell between one and two (see Fig 2 in [25]). TL has also been verified for non-biological variables such as crime incidents [26], stock illiquidity [27], prime numbers [28], and tornado outbreaks [29]; in this last case, the slope exceeded four. Several models have been proposed to study the biological or statistical mechanisms of TL [30–32].…”