Abstract

This study tested for both unit root and chaos in the daily returns on Istanbul Stock Exchange (ISE 100) all share equity indices from 01.01.1990 to 07.10.2009. In order to detect unit root, we applied Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test statistics and to compute maximal Lyapunov exponent (LE), we applied Kantz’s algorithm, Kantz (1994) Physics Letters A 185, 77-87. Our results have uncovered the chaotic behavior of daily returns on ISE 100 index. We concluded that by reverse engineering, the statistical properties of chaos enable us to achieve potential out-of-sample predictability for limited period, namely, until the process loses its stability. Furthermore, maximal Lyapunov exponent can be used to explain stock traders’ buy and sell mechanism and to achieve alternative trading rule, leading to observed chaotic behavior.

Key words: Chaos, Lyapunov exponent, efficient market hypothesis, stock return, predictability, trading rule, unit-root analysis.