Nonlinearities and nonstationarities in stock returns

This article addresses the question of whether recent findings of nonlinearities in high-frequency financial time series have been contaminated by possible shifts in the distribution of the data. It applies a recursive version of the Brouk-Dechert-Scheinkman statistic to daily data on two stock-market indexes between January 1980 and December 1990. It is shown that October 1987 is highly influential in the characterization of the stock-market dynamics and appears to correspond to a shift in the distribution of stock returns. Sampling experiments show that simple linear processes with shifts in variance can replicate the behavior of the tests, but autoregressive conditional hereroscedastic filters are unable to do so.