Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 120518, 12 pages
http://dx.doi.org/10.1155/2012/120518
Research Article

Power Law Analysis of Financial Index Dynamics

J. Tenreiro Machado,1 Fernando B. Duarte,2 and Gonçalo Monteiro Duarte3

1Department of Electrical Engineering, Institute of Engineering, 4200-072 Porto, Portugal
2Faculty of Engineering and Natural Sciences, Lusofona University, 1749-024 Lisbon, Portugal
3Faculty of Economics and Management, Lusofona University, 1749-024 Lisbon, Portugal

Received 17 February 2012; Accepted 15 May 2012

Academic Editor: Daniele Fournier-Prunaret

Copyright © 2012 J. Tenreiro Machado et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Power law (PL) and fractional calculus are two faces of phenomena with long memory behavior. This paper applies PL description to analyze different periods of the business cycle. With such purpose the evolution of ten important stock market indices (DAX, Dow Jones, NASDAQ, Nikkei, NYSE, S&P500, SSEC, HSI, TWII, and BSE) over time is studied. An evolutionary algorithm is used for the fitting of the PL parameters. It is observed that the PL curve fitting constitutes a good tool for revealing the signal main characteristics leading to the emergence of the global financial dynamic evolution.