Evolving multi-humped distributions of stock market prices-An empirical observation of nonequiliÂbrium behavior

The standard random walk model of the stock market is based on the observation that the distribution of logarithmic price changes is unimodal and near-Gaussian. The present study reported here of the S&P 500 price index reveals, however, a multi-humped distribution of price deviations around a long-term growth trend. Histograms observed through a shifting finite time-window show evolving patterns of price deviations and different phases of business cycles. The patterns recover the experience of American Business cycles during the period of study. The authors argue that the information obtained by observing multi-humped distributions is more relevant and useful for modeling the market behavior than the information based on a static unimodal distribution. Nonlinear dynamics provides a means for modeling multi-humped distributions that may evolve.