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Exact results for the roughness of a finite size random walk

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  • Alfi, V.
  • Coccetti, F.
  • Marotta, M.
  • Petri, A.
  • Pietronero, L.

Abstract

We consider the role of finite size effects on the value of the effective Hurst exponent H. This problem is motivated by the properties of the high-frequency daily stock-prices. For a finite size random walk we derive some exact results based on Spitzer's identity. The conclusion is that finite size effects strongly enhance the value of H and the convergency to the asymptotic value (H=12) is rather slow. This result has a series of conceptual and practical implication which we discuss.

Suggested Citation

  • Alfi, V. & Coccetti, F. & Marotta, M. & Petri, A. & Pietronero, L., 2006. "Exact results for the roughness of a finite size random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 127-131.
    • Handle: RePEc:eee:phsmap:v:370:y:2006:i:1:p:127-131
    DOI: 10.1016/j.physa.2006.04.020
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    References listed on IDEAS

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    1. Grech, D & Mazur, Z, 2004. "Can one make any crash prediction in finance using the local Hurst exponent idea?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 133-145.
    2. Cajueiro, Daniel O & Tabak, Benjamin M, 2004. "The Hurst exponent over time: testing the assertion that emerging markets are becoming more efficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 521-537.
    3. Matteo, T. Di & Aste, T. & Dacorogna, Michel M., 2005. "Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 827-851, April.
    4. Carbone, A. & Castelli, G. & Stanley, H.E., 2004. "Time-dependent Hurst exponent in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 267-271.
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