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Scaling transformation and probability distributions for financial time series

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  • Marc-Etienne Brachet
  • Erik Taflin
  • Jean Marcel Tcheou

Abstract

The price of financial assets are, since Bachelier, considered to be described by a (discrete or continuous) time sequence of random variables, i.e a stochastic process. Sharp scaling exponents or unifractal behavior of such processes has been reported in several works. In this letter we investigate the question of scaling transformation of price processes by establishing a new connexion between non-linear group theoretical methods and multifractal methods developed in mathematical physics. Using two sets of financial chronological time series, we show that the scaling transformation is a non-linear group action on the moments of the price increments. Its linear part has a spectral decomposition that puts in evidence a multifractal behavior of the price increments.

Suggested Citation

  • Marc-Etienne Brachet & Erik Taflin & Jean Marcel Tcheou, 1999. "Scaling transformation and probability distributions for financial time series," Papers cond-mat/9905169, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/9905169
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    Cited by:

    1. Bacry, E. & Delour, J. & Muzy, J.F., 2001. "Modelling financial time series using multifractal random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 84-92.
    2. Struzik, Zbigniew R., 2003. "Econonatology: the physics of the economy in labour," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 344-351.
    3. Struzik, Zbigniew R. & Siebes, Arno P.J.M., 2002. "Wavelet transform based multifractal formalism in outlier detection and localisation for financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 388-402.

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