Tsallis Entropy: Do the Market Size and Liquidity Matter?

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

See all articles by Constantin Gurdgiev

Constantin Gurdgiev

Monfort College of Business, University of Northern Colorado; Trinity Business School, Trinity College, Dublin

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)

Monfort College of Business, University of Northern Colorado ( email )

Kepner Hall
800 17th Street
Greeley, CO 80639
United States
80639 (Fax)

Trinity Business School, Trinity College, Dublin ( email )

Aras an Phiarsaigh
College Green
Dublin, Leinster D2
Ireland

Gerard Harte

Trinity College (Dublin) ( email )

2-3 College Green
Dublin, Leinster D2
Ireland

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