Available online at www.sciencedirect.com Physica A 324 (2003) 183–188 www.elsevier.com/locate/physa Scaling behaviors in dierently developed markets T. Di Matteo a; b; ∗ , T. Aste a , M.M. Dacorogna c a Applied Mathematics, Research School of Physical Sciences, Australian National University, 0200 Canberra, Australia b INFM - Dipartimento di Fisica “E.R. Caianiello”, Universiti a degli Studi di Salerno, 84081 Baronissi (SA), Italy c Converium Ltd, General Guisan - Quai 26, 8022 Zurich, Switzerland Abstract Scaling properties of four dierent stock market indices are studied in terms of a generalized Hurst exponent approach. We nd that the deviations from pure Brownian motion behavior are associated with the degrees of development of the markets and we observe strong dierentiations in the scaling properties of markets at dierent development stage. c  2003 Elsevier Science B.V. All rights reserved. 1. Introduction The scaling properties in time series have been studied in the literature by means of a great variety of techniques [1–11]. Historically, one of the most eective techniques was the rescaled range statistical analysis rst introduced by Harold Edwin Hurst to describe the long-term dependence of water levels in rivers and reservoirs [12]. This analysis provides a sensitive method for revealing long-run correlations in random processes. What especially makes the Hurst analysis appealing is that all these information about a complex signal are contained in one parameter only: the Hurst exponent. On the other hand, one of the weaknesses of the original method is that it relies on maximum and minimum data, which makes it very sensitive to outliers. In order to study the multi-fractal features of the data, here we use an alternative method to the original approach of Hurst. This method is applied to the study of the scaling properties of * Corresponding author. Applied Mathematics, Research School of Physical Sciences, Australian National University, Canberra 0200, Australia. 0378-4371/03/$-see front matter c  2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0378-4371(02)01996-9