Scaling Power Laws in the Sao Paulo Stock Exchange

Iram Gleria, Catholic University of Brasilia
Raul Matsushita, University of Brasilia
Sergio Da Silva, University of Brasilia

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Abstract

The scaling of the probability distribution of the Sao Paulo Stock Exchange index is shown to be described by a Levy stable stochastic process for the modal region of the distribution. The truncated Levy process is characterized by a scaling index of 1.66. Scaling power laws are also shown to be present in the mean and standard deviation of the series as the time horizon is increased. A power law is also found for the autocorrelation time of the natural logs of the index series. The deviations from the line that best fits the natural logs of the series are also found to be short range autocorrelated and to follow an exponential decay.

Cited in Mandelbrot's last book:

Richard L. Hudson and Benoit B. Mandelbrot (2004) The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward. New York: Basic Books