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Tsallis entropy: Do the market size and liquidity matter?

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  • Gurdgiev, Constantin
  • Harte, Gerard

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.

Suggested Citation

  • Gurdgiev, Constantin & Harte, Gerard, 2016. "Tsallis entropy: Do the market size and liquidity matter?," Finance Research Letters, Elsevier, vol. 17(C), pages 151-157.
    • Handle: RePEc:eee:finlet:v:17:y:2016:i:c:p:151-157
    DOI: 10.1016/j.frl.2016.03.006
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    References listed on IDEAS

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    1. Onali, Enrico & Goddard, John, 2011. "Are European equity markets efficient? New evidence from fractal analysis," International Review of Financial Analysis, Elsevier, vol. 20(2), pages 59-67, April.
    2. Fredrick Michael & M. D. Johnson, 2001. "Financial Market Dynamics," Papers cond-mat/0108017, arXiv.org.
    3. Silvio M. Duarte Queiros & Constantino Tsallis, 2004. "Bridging the ARCH model for finance and nonextensive entropy," Papers cond-mat/0401181, arXiv.org, revised Jan 2004.
    4. Stavroyiannis, S. & Makris, I. & Nikolaidis, V., 2010. "Non-extensive properties, multifractality, and inefficiency degree of the Athens Stock Exchange General Index," International Review of Financial Analysis, Elsevier, vol. 19(1), pages 19-24, January.
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    More about this item

    Keywords

    High frequency trading; Power laws; Tsallis distribution; Hurst exponent;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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