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GENERALIZED(m, k)-ZipfLAW FOR FRACTIONAL BROWNIAN MOTION-LIKE TIME SERIES WITH OR WITHOUT EFFECT OF AN ADDITIONAL LINEAR TREND

Author

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  • PH. BRONLET

    (SUPRAS and GRASP, B5, Sart Tilman Campus, B-4000 Liège, Euroland)

  • M. AUSLOOS

    (SUPRAS and GRASP, B5, Sart Tilman Campus, B-4000 Liège, Euroland)

Abstract

We have translated fractional Brownian motion (FBM) signals into a text based on two "letters", as if the signal fluctuations correspond to a constant stepsize random walk. We have applied the Zipf method to extract the ζ′ exponent relating the word frequency and its rank on a log–log plot. We have studied the variation of the Zipf exponent(s) giving the relationship between the frequency of occurrence of words of lengthm

Suggested Citation

  • Ph. Bronlet & M. Ausloos, 2003. "GENERALIZED(m, k)-ZipfLAW FOR FRACTIONAL BROWNIAN MOTION-LIKE TIME SERIES WITH OR WITHOUT EFFECT OF AN ADDITIONAL LINEAR TREND," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 351-365.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:03:n:s0129183103004528
    DOI: 10.1142/S0129183103004528
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    References listed on IDEAS

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    1. Perez, A.A, 2001. "Comment on “On the multinomial logic model” [Physica A 269 (1999) 9–15]," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(3), pages 606-606.
    2. Hoover, W.G., 1995. "Comment on “Two disks in a box” [R.J. Speedy, Physica A 210 (1994) 341]," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 216(1), pages 195-195.
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    Cited by:

    1. Claudiu Vinte & Marcel Ausloos & Titus Felix Furtuna, 2022. "A Volatility Estimator of Stock Market Indices Based on the Intrinsic Entropy Model," Papers 2205.01370, arXiv.org.
    2. Ausloos, M. & Bronlet, Ph., 2003. "Strategy for investments from Zipf law(s)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 30-37.
    3. Marcel Ausloos, 2013. "Econophysics: Comments on a Few Applications, Successes, Methods and Models," IIM Kozhikode Society & Management Review, , vol. 2(2), pages 101-115, July.
    4. M. Ausloos & Ph. Bronlet, 2006. "Risk portofolio management under Zipf analysis based strategies," Springer Books, in: Hideki Takayasu (ed.), Practical Fruits of Econophysics, pages 257-261, Springer.

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