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

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.