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Zbl 1248.91058
Machado, J.Tenreiro; Duarte, Fernando B.; Duarte, Gonçalo Monteiro
Power law analysis of financial index dynamics. (English)
[J] Discrete Dyn. Nat. Soc. 2012, Article ID 120518, 12 p. (2012). ISSN 1026-0226; ISSN 1607-887X/e

Summary: 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\& P 500, 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.

MSC 2000:: *91B62 Dynamic economic models etc.
91B82 Statistical methods in economics
91B84 Economic time series analysis
26A33 Fractional derivatives and integrals (real functions)
62P05 Appl. of statistics to actuarial sciences and financial mathematics

Keywords: power law analysis; stock market indices

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