Lévy flights, autocorrelation, and slow convergence

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

Physica A: Statistical Mechanics and its Applications, 2004, vol. 337, issue 3, 369-383

Abstract: Previously we have put forward that the sluggish convergence of truncated Lévy flights to a Gaussian (Phys. Rev. Lett. 73 (1994) 2946) together with the scaling power laws in their probability of return to the origin (Nature 376 (1995) 46) can be explained by autocorrelation in data (Physica A 323 (2003) 601; Phys. Lett. A 315 (2003) 51). A purpose of this paper is to improve and enlarge the scope of such a result. The role of the autocorrelations in the convergence process as well as the problem of establishing the distance of a given distribution to the Gaussian are analyzed in greater detail. We show that whereas power laws in the second moment can still be explained by linear correlation of pairs, sluggish convergence can now emerge from nonlinear autocorrelations. Our approach is exemplified with data from the British pound–US dollar exchange rate.

Keywords: Lévy flights; Autocorrelation; Slow convergence; Foreign exchange rates (search for similar items in EconPapers)
Date: 2004
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037843710400175X
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
Working Paper: Levy Flights, Autocorrelation, and Slow Convergence (2004)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:337:y:2004:i:3:p:369-383

DOI: 10.1016/j.physa.2004.02.002

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().