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The Levy sections theorem revisited

Author

Listed:
  • Figueiredo, Annibal
  • Gleria, Iram
  • Matsushita, Raul
  • Da Silva, Sergio

Abstract

This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end our extension of the theorem provides an approach that is simpler than the more common explicit modeling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analyzing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets.

Suggested Citation

  • Figueiredo, Annibal & Gleria, Iram & Matsushita, Raul & Da Silva, Sergio, 2006. "The Levy sections theorem revisited," MPRA Paper 1983, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:1983
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    File URL: https://mpra.ub.uni-muenchen.de/1983/1/MPRA_paper_1983.pdf
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    References listed on IDEAS

    as
    1. Figueiredo, Annibal & Gleria, Iram & Matsushita, Raul & Da Silva, Sergio, 2006. "Nonidentically distributed variables and nonlinear autocorrelation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 171-180.
    2. Helyette Geman & Dilip B. Madan & Marc Yor, 2001. "Asset Prices Are Brownian Motion: Only In Business Time," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 4, pages 103-146, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Figueiredo, Annibal & Matsushita, Raul & Da Silva, Sergio & Serva, Maurizio & Viswanathan, Gandhi & Nascimento, Cesar & Gleria, Iram, 2007. "The Levy sections theorem: an application to econophysics," MPRA Paper 3810, University Library of Munich, Germany.

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    More about this item

    Keywords

    Econophysics; Levy sections;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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