Generalized entropy approach to stable Levy distributions with financial application

Employing the generalized entropy introduced by Tsallis, we propose a new method to estimate the scaling index of the stable Levy distribution. We investigate the scaling behavior of the daily Nikkei average sampled from January 1991 to December 2000 for the time intervals up to 75 days from two aspects, self-similarity of the distribution and long-range dependence in the autocorrelation function. It is found that the theoretically estimated scaling index mu* = 1.59 and Hurst exponent H* = 0.629 agree well with mu = 1.50 and H = 0.617 obtained from the measured data, respectively, suggesting the usefulness and fitness of the present method. (C) 2002 Elsevier Science B.V. All rights reserved.