Nonlinear Dynamics in Real-Time Equity Market Indices: Evidence from the UK

Abstract

This paper tests for the presence of nonlinear dependence and chaos in real-time returns on the U.K. FTSE-100 Index, using a six month sample of about 60,000 observations, at a range of frequencies from 1-minute to 60-minutes. We use the frequency domain Hinich (1982) and the BDS (1986) tests for nonlinearity. In the first place, we apply these tests to the residuals from a standard ARMA filter. We find clear evidence of nonlinearity. We then follow other researchers in this field by applying the same tests to the residuals from a GARCH process fitted to the data, to find out whether or not the nonlinearity can be explained by this type of model. In the event, our results suggest that GARCH can explain some but not all of the observed nonlinear dependence. In the second half of the paper, we estimate the Lyapunov exponents to test directly for chaos (i.e. sensitivity to initial conditions). We use two Jacobian based techniques suitable for noisy data sets. The first, the Nychka, Gallant, Ellner, McCaffrey (1992) method uses neural nets, while the second technique utilizes higher order local neighbourhood-to-neighbourhood mappings (Brown et al (1991)) to estimate the Jacobian matrices, as in Zeng, Pielke and Eyckholt (1992). Our results indicate the presence of non-linear dependence in high frequency FTSE-100 returns. However we find very little evidence that they could be characterised by a low-dimensional chaotic process. Instead, the Lyapunov exponent estimates appear to be extremely sensitive to the precise methods used in estimation.

JEL Classification: C13, G12