Scaling transformation and probability distributions for financial time series
AbstractThe 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.
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Bibliographic InfoPaper provided by EconWPA in its series GE, Growth, Math methods with number 9901003.
Length: 12 pages
Date of creation: 25 Jan 1999
Date of revision:
Note: Type of Document - PostScript; prepared on TeX; to print on PostScript-color; pages: 12; figures: included-EPS
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multifractal; scaling; exchange rate; stock index; non-linear group action;
Find related papers by JEL classification:
- C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
- D5 - Microeconomics - - General Equilibrium and Disequilibrium
- D9 - Microeconomics - - Intertemporal Choice and Growth
This paper has been announced in the following NEP Reports:
- NEP-ALL-1999-02-15 (All new papers)
- NEP-CMP-1999-02-22 (Computational Economics)
- NEP-ECM-1999-02-22 (Econometrics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation for Research in Economics, Yale University.
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