Why do Hurst Exponents of Traded Value Increase as the Logarithm of Company Size?

Eisler, Zoltán; Kertész, János

doi:10.1007/978-88-470-0502-0_5

Cited by 7 publications

(7 citation statements)

References 18 publications

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“…Taylor's law of temporal fluctuation scaling has also been observed in diverse disciplines [6], such as traffic fluxes recorded at individual nodes in transportation networks (the number of bytes on Internet, the stream flow in river networks, the number of cars on highways) [18][19][20][21], gene expression time series from yeast and human organisms [22], gene network of yeast [23], trading activities in stock markets [24][25][26][27][28][29][30][31][32], application installations [33], quotation activities and transaction activities in the foreign exchange market [34], species abundance [15,35] We notice that the quantities investigated in the literature of Taylor's law are usually additive, that is, It is unclear if Taylor's law holds for non-additive quantities. In this paper, we perform a mean-variance analysis on the high-frequency illiquidity time series of Chinese stocks listed on the Shenzhen Stock Exchange (SZSE) and the Shanghai Stock Exchange (SHSE).…”

Section: Introductionmentioning

confidence: 99%

Taylor’s Law of Temporal Fluctuation Scaling in Stock Illiquidity

Cai

Zhou

2016

Fluct. Noise Lett.

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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.

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Section: Introductionmentioning

confidence: 99%

Taylor’s Law of Temporal Fluctuation Scaling in Stock Illiquidity

Cai

Zhou

2016

Fluct. Noise Lett.

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“…The method of fluctuation analysis is a classical approach to extract the Hurst exponent of time series [179], which has been applied extensively in econophysics [180][181][182][183][184]. The fluctuation function can be calculated as follows,…”

Section: Multifractal Fluctuation Analysis (Mf-fa)mentioning

confidence: 99%

Multifractal analysis of financial markets

Jiang,

Xie,

Zhou

et al. 2018

Preprint

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Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.

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“…Thus we should be careful when we apply concepts like scaling and universality to complex systems. [30]…”

Section: ) the Coexistence With Pseudo Long Range Dependencementioning

confidence: 99%

Fluctuations and pseudo long range dependence in network flows: A non-stationary Poisson process model

Chen¹,

Li²,

Zhang³

et al. 2009

Chinese Phys. B

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In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) ⟨Fi⟩ of the i-th node and its variance σi as σi α ⟨Fi⟩α. Such scaling laws are found to be prevalent both in natural and man-made network systems, but the understanding of their origins still remains limited. This paper proposes a non-stationary Poisson process model to give an analytical explanation of the non-universal scaling phenomenon: the exponent α varies between 1/2 and 1 depending on the size of sampling time window and the relative strength of the external/internal driven forces of the systems. The crossover behaviour and the relation of fluctuation scaling with pseudo long range dependence are also accounted for by the model. Numerical experiments show that the proposed model can recover the multi-scaling phenomenon.

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Why do Hurst Exponents of Traded Value Increase as the Logarithm of Company Size?

Cited by 7 publications

References 18 publications

Taylor’s Law of Temporal Fluctuation Scaling in Stock Illiquidity

Taylor’s Law of Temporal Fluctuation Scaling in Stock Illiquidity

Multifractal analysis of financial markets

Fluctuations and pseudo long range dependence in network flows: A non-stationary Poisson process model

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