Self-criticality and stochasticity of an S&P 500 index time series

In this paper, three time series representative of the daily high, low and closing prices of S&P 500 index time series, as from 1 December 1988 to 1 A pril 1998 are studied. The hypothesis advanced by Osborne that the stock ma rket time series satisfy a log-normal distribution is rejected. The self-cr itical behavior of these time series is investigated. A fractional Brownian motion model for such time series is supported. Arguments are directed tow ards a negation of a chaotic explanation of these time series. (C) 2000 Els evier Science Ltd. All rights reserved.