Tsallis Entropy: Do the Market Size and Liquidity Matter?

12 Pages Posted: 11 Oct 2014 Last revised: 11 Jan 2016

Constantin Gurdgiev

Trinity College, Dublin; Middlebury Institute of International Studies at Monterey (MIIS)

Gerard Harte

Trinity College (Dublin)

Date Written: January 10, 2016

Abstract

One of the key assumptions in financial markets analysis is that of normally distributed returns and market efficiency. Both of these assumptions have been extensively challenged in the literature. In the present paper, we examine returns for a number of FTSE 100 and AIM stocks and indices based on maximising the Tsallis entropy. This framework allows us to show how the distributions evolve and scale over time. Classical theory dictates that if markets are efficient then the time variant parameter of the Tsallis distribution should scale with a power equal to 1, or normal diffusion. We find that for the majority of securities and indices examined, the Tsallis time variant parameter is scaled with super diffusion of greater than 1. We further evaluated the fractal dimensions and Hurst exponents and found that a fractal relationship exists between main equity indices and their components.

Keywords: High Frequency Trading, Power Laws, Tsallis Distribution, Chaos Dynamics, Hurst Exponent

JEL Classification: G00, G12, G14

Suggested Citation

Gurdgiev, Constantin and Harte, Gerard, Tsallis Entropy: Do the Market Size and Liquidity Matter? (January 10, 2016). Available at SSRN: https://ssrn.com/abstract=2507977 or http://dx.doi.org/10.2139/ssrn.2507977

Constantin Gurdgiev (Contact Author)

Trinity College, Dublin ( email )

Trinity College
Dublin 2

Middlebury Institute of International Studies at Monterey (MIIS) ( email )

460 Pierce St
Monterey, CA 93940
United States

Gerard Harte

Trinity College (Dublin) ( email )

2-3 College Green
Dublin 2, Leinster 2
Ireland

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