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Measuring subtle effects of persistence in the stock market dynamics

Rafał Rak 1Stanisław Drożdż 1,2Jarosław Kwapień 2

1. University of Rzeszow, Institute of Physics, Rejtana 16, Rzeszów 35-310, Poland
2. Polish Academy of Sciences, Institute of Nuclear Physics (IFJ PAN), Radzikowskiego 152, Kraków 31-342, Poland

Abstract

The conventional formal tool to detect effects of the financial persistence is in terms of the Hurst exponent. A typical corresponding result is that its value comes out close to 0.5, as characteristic for geometric Brownian motion, with at most small departures from this value in either direction depending on the market and on the time scales involved. We study the high frequency price changes on the American and on the German stock markets. For both corresponding indices, the Dow Jones and the DAX respectively, the Hurst exponent analysis results in values close to 0.5. However, by decomposing the market dynamics into pairs of steps such that an elementary move up (down) is followed by another move up (down) and explicitely counting the resulting conditional probabilities we find values typically close to 60%. This effect of persistence is particularly visible on the short time scales ranging from 1 up to 2 minutes, decreasing gradually to 50% and even significantly below this value on the larger time scales. This indicates a subtle nature of the financial persistence whose characteristics escape detection within the conventional Hurst exponent formalism.

 

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Related papers

Presentation: oral at Symposium on Econo- and Sociophysics 2004, by Rafał Rak
See On-line Journal of Symposium on Econo- and Sociophysics 2004

Submitted: 2004-10-12 19:21
Revised:   2009-06-08 12:55