Exponentially damped Lévy flights

Raul Matsushita, Pushpa Rathie and Sergio Da Silva

Physica A: Statistical Mechanics and its Applications, 2003, vol. 326, issue 3, 544-555

Abstract: 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.

Keywords: Lévy flights; Foreign exchange rates (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (14)

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Related works:
Working Paper: Exponentially Damped Levy Flights (2004)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:326:y:2003:i:3:p:544-555

DOI: 10.1016/S0378-4371(03)00363-7

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