No evidence of chaos but some evidence of dependence in the US stock market

This paper uses recent advances in the field of applied econometrics and tools from dynamical systems theory to test for random walks and chaos in the US stock market, using daily observations on the Dow Jones Industrial Average (from January 3, 1928 to October 18, 2000––a total of 18,490 observations). In doing so, we follow the recent contribution by Whang and Linton [J Econometr 91 (1999) 1] and construct the standard error for the Nychka et al. [J Roy Statist Soc B 54 (1992) 399] dominant Lyapunov exponent, thereby providing a statistical test of chaos. We find statistically significant evidence against low-dimensional chaos and point to the use of stochastic models and statistical inference in the modeling of asset markets.