Exponentially Damped Levy Flights
Since real processes seem to departure from standard Lévy distributions, modifications to the latter have been suggested in literature. These include (abruptly) truncated (Phys. Rev. Lett. 73 (1994) 2946), smoothly truncated (Phys. Rev. E 52 (1995) 1197; Phys. Lett. A 266 (2000) 282) and gradually truncated Lévy flights (Physica A 268 (1999) 231; Physica A 275 (2000) 531). We put forward what we call an exponentially damped Lévy flight which encompasses the previous cases. In the presence of increasing and positive feedbacks, our distribution is assumed to deviate from the Lévy in both a smooth and gradual fashion. We estimate the truncation parameters by nonlinear least squares to optimally fit the distribution tails. That is a novel approach for estimating parameters α and γ of the Lévy. The method is illustrated with daily data on exchange rates for 15 countries against the US dollar. Our results show that the exponentially damped Lévy flight fits the data well when increasing and positive deviations are present.
(This abstract was borrowed from another version of this item.)
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 1-394.
- 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.
- Andrew W. Lo & A. Craig MacKinlay, 1987. "Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test," NBER Working Papers 2168, National Bureau of Economic Research, Inc.
- Tom Doan, "undated". "VRATIO: RATS procedure to implement variance ratio unit root test procedure," Statistical Software Components RTS00231, Boston College Department of Economics.
- Sergio Da Silva, 2004.
"Autocorrelation as a Source of Truncated Levy Flights in Foreign Exchange Rates,"
- Figueiredo, Annibal & Gleria, Iram & Matsushita, Raul & Da Silva, Sergio, 2003. "Autocorrelation as a source of truncated Lévy flights in foreign exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 601-625.
- 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.
- repec:ebl:ecbull:v:7:y:2002:i:3:p:1-12 is not listed on IDEAS
- Gupta, Hari M. & Campanha, José R., 1999. "The gradually truncated Lévy flight for systems with power-law distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(1), pages 231-239.
- Gupta, Hari M. & Campanha, José R., 2000. "The gradually truncated Lévy flight: stochastic process for complex systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 275(3), pages 531-543.
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpfi:0406002. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)
If references are entirely missing, you can add them using this form.