Physica A 270 (1999) 526–542 www.elsevier.com/locate/physa Precise (m; k )-Zipf diagram analysis of mathematical and nancial time series when m = 6, k =2 M. Ausloos a , K. Ivanova b; ∗ a SUPRAS and GRASP, Institut de Physique B5, Universit e de Li ege, B-4000 Li ege, Belgium b Department of Meteorology, Pennsylvania State University, University Park, PA 16802, USA Received 27 March 1999 Abstract For studying short-range time correlations in nancial 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  exponent of Zipf plots does not seem to be substantiated here. c  1999 Elsevier Science B.V. All rights reserved. PACS: 05.45.D; 05.45.T; 05.40.J; 05.20 Keywords: Fractal non linear dynamics; Time series analysis; Brownian motion; Classical statistical mechanics 1. Introduction The Zipf method has been used by Stanley et al. [1] in order to examine the size distribution of rms and by Vandewalle and Ausloos [2] in order to sort out whether for a given stock price some correlation could be found at short times. On the other * Corresponding author. Permanent address: Institute of Electronics, Bulgarian Academy of Sciences, Soa 1784, Bulgaria. E-mail addresses: ausloos@gw.unipc.ulg.ac.be (M. Ausloos), kristy@essc.psu.edu (K. Ivanova) 0378-4371/99/$ - see front matter c  1999 Elsevier Science B.V. All rights reserved. PII: S0378-4371(99)00178-8