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Power law analysis of financial index dynamics. (English) Zbl 1248.91058
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:
91B62Growth models in economics
91B82Statistical methods in economics; economic indices and measures
91B84Economic time series analysis
26A33Fractional derivatives and integrals (real functions)
62P05Applications of statistics to actuarial sciences and financial mathematics