Instability and chaotic dynamics in stock returns

Abstract

In this paper we examine certain properties of the Dow Jones and the Nikkey indices, investigating the existence of stochastic and deterministic nonlinear structures. Using the detrended fluctuation analysis, we construct a local measurement of randomness which identifies some extreme events and their impact on the randomness of the systems. Our results suggest no evidence of chaos in the data. In fact, GARCH processes explain most of the nonlinear dependence in the Dow Jones daily returns and the estimated Kolmogorov entropy for the Nikkey index diverges, conversely to what one would expect if the data followed a chaotic dynamics.