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Autocorrelation as a source of truncated Lévy flights in foreign exchange rates

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

We suggest that the ultraslow speed of convergence associated with truncated Lévy flights (Phys. Rev. Lett. 73 (1994) 2946) may well be explained by autocorrelations in data. We show how a particular type of autocorrelation generates power laws consistent with a truncated Lévy flight. Stock exchanges have been suggested to be modeled by a truncated Lévy flight (Nature 376 (1995) 46; Physica A 297 (2001) 509; Econom. Bull. 7 (2002) 1). Here foreign exchange rate data are taken instead. Scaling power laws in the “probability of return to the origin” are shown to emerge for most currencies. A novel approach to measure how distant a process is from a Gaussian regime is presented.

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Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 323 (2003)
Issue (Month): C ()
Pages: 601-625

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Handle: RePEc:eee:phsmap:v:323:y:2003:i:c:p:601-625
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  1. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
  2. Sergio Da Silva & Raul Matsushita & Iram Gleria, 2002. "Scaling power laws in the Sao Paulo Stock Exchange," Economics Bulletin, AccessEcon, vol. 7(3), pages 1-12.
  3. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
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