Levy flights, autocorrelation, and slow convergence

被引：10

作者：

Figueiredo, A

Gleria, I

Matsushita, R

Da Silva, S ^{[1
]}

机构：

[1] Univ Fed Rio Grande Sul, Dept Econ, BR-90040000 Porto Alegre, RS, Brazil

[2] Univ Brasilia, Dept Phys, BR-70910900 Brasilia, DF, Brazil

[3] Fed Univ Alagoas, Dept Phys, BR-57072970 Maceio, AL, Brazil

[4] Univ Brasilia, Dept Stat, BR-70910900 Brasilia, DF, Brazil

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2004年 / 337卷 / 3-4期

关键词：

Levy flights; autocorrelation; slow convergence; foreign exchange rates;

D O I：

10.1016/j.physa.2004.02.002

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Previously we have put forward that the sluggish convergence of truncated Levy 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 taws 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. (C) 2004 Elsevier B.V. All rights reserved.

引用

页码：369 / 383

页数：15

共 16 条

[11] A NOTE ON THE ALMOST SURE CENTRAL-LIMIT-THEOREM FOR WEAKLY DEPENDENT RANDOM-VARIABLES [J].