Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets
- *Department of Physics and
- †Texas Center for Superconductivity, University of Houston, Houston, TX 77204;
- ‡J. E. Cairnes Graduate School of Business and Public Policy, National University of Ireland, Galway, Ireland; and
- §Institute of Fundamental Studies, Kandy, Sri Lanka
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Communicated by Mitchell J. Feigenbaum, The Rockefeller University, New York, NY, September 13, 2007 (received for review November 24, 2006)
Abstract
Fat-tailed distributions have been reported in fluctuations of financial markets for more than a decade. Sliding interval techniques used in these studies implicitly assume that the underlying stochastic process has stationary increments. Through an analysis of intraday increments, we explicitly show that this assumption is invalid for the Euro–Dollar exchange rate. We find several time intervals during the day where the standard deviation of increments exhibits power law behavior in time. Stochastic dynamics during these intervals is shown to be given by diffusion processes with a diffusion coefficient that depends on time and the exchange rate. We introduce methods to evaluate the dynamical scaling index and the scaling function empirically. In general, the scaling index is significantly smaller than previously reported values close to 0.5. We show how the latter as well as apparent fat-tailed distributions can occur only as artifacts of the sliding interval analysis.
Footnotes
- ¶To whom correspondence should be addressed. E-mail: gemunu{at}uh.edu
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Author contributions: G.H.G. designed research; K.E.B. performed research; J.L.M. and G.H.G. contributed new reagents/analytic tools; K.E.B. analyzed data; and K.E.B., J.L.M., and G.H.G. wrote the paper.
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The authors declare no conflict of interest.
- © 2007 by The National Academy of Sciences of the USA
