Precise (m,k)-Zipf diagram analysis of mathematical and financial time series when m=6, k=2

Marcel Ausloos and K. Ivanova

Physica A: Statistical Mechanics and its Applications, 1999, vol. 270, issue 3, 526-542

Abstract: For studying short-range time correlations in financial signals, we have envisaged to combine the Zipf method and the i-variability diagrams (VD) as useful tools. The 2-VD describes the local curvature short-range correlations. We have resulted into ranking the 2-VD data according to their frequency of occurrence. After having tested the ideas and estimated the error bars on a Brownian motion signal, we have examined two stocks, i.e. SGP and OXHP closing price and volume of transaction long series. A precise (m,k)-Zipf diagram analysis when m=6,k=2 has been shown to lead to a non-immediate information on the signal behavior, even taking into account error bars. The set of curvatures (translated into “words”) indicates a Brownian motion-like set for the closing price local curvature of such signals over a 6 day span. Moreover, it has been shown that the conjecture about a simple relationship between the Hurst exponent H and the ζ exponent of Zipf plots does not seem to be substantiated here.

Keywords: Fractal non linear dynamics; Time series analysis; Brownian motion; Classical statistical mechanics (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:270:y:1999:i:3:p:526-542

DOI: 10.1016/S0378-4371(99)00178-8

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