Uncovering Nonlinear Structure in Real-Time Stock Market Indices

This paper tests for the presence of nonlinear dependence and chaos in real-time returns on four of the world's major stock market indices: the FTSE-100, the Samp;P 500, the Nikkei 225 and the DAX. Our results suggest that GARCH-type models can explain some but not all of the observed nonlinear dependence. The neural network-based test for nonlinearity introduced by Lee, White and Granger (1993) provides conclusive evidence of a persistent nonlinear structure in the series. We also estimate Lyapunov exponents in order to test directly for chaos using both the Nychka, Ellner, Gallant, McCaffrey (1992) and the Zeng, Pielke and Eyckholt (1992) methods. We find that none of the series seem to be characterised by a low-dimensional chaotic process. Instead, the Lyapunov exponent estimates appear to be extremely sensitive to the parameter values used in estimation, a fact which in itself may be an indication that the data are dominated by a stochastic component