Scaling transformation and probability distributions for financial time series

Marc-Etienne Brachet, Erik Taflin and Jean Marcel Tcheou
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Marc-Etienne Brachet: Laboratoire de Physique Statistique, CNRS, ENS, France
Erik Taflin: Direction Scientifique, AXA-UAP, France
Jean Marcel Tcheou: Laboratoire de Physique Statistique, ENS, France; Direction Scientifique, AXA-UAP, France

GE, Growth, Math methods from University Library of Munich, Germany

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.

Keywords: multifractal; scaling; exchange rate; stock index; non-linear group action (search for similar items in EconPapers)
JEL-codes: C6 D5 D9 (search for similar items in EconPapers)
Pages: 12 pages
Date: 1999-01-25
New Economics Papers: this item is included in nep-cmp and nep-ecm
Note: Type of Document - PostScript; prepared on TeX; to print on PostScript-color; pages: 12; figures: included-EPS
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Citations: View citations in EconPapers (3)

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