Computational Economics

, Volume 21, Issue 3, pp 257–276

Is it Possible to Study Chaotic and ARCH Behaviour Jointly? Application of a Noisy Mackey–Glass Equation with Heteroskedastic Errors to the Paris Stock Exchange Returns Series

  • Catherine Kyrtsou
  • Michel Terraza

DOI: 10.1023/A:1023939610962

Cite this article as:
Kyrtsou, C. & Terraza, M. Computational Economics (2003) 21: 257. doi:10.1023/A:1023939610962


Most recent empirical works that apply sophisticated statistical proceduressuch as a correlation-dimension method have shown that stock returns arehighly complex. The estimated correlation dimension is high and there islittle evidence of low-dimensional deterministic chaos. Taking the complexbehaviour in stock markets into account, we think it is more robust than thetraditional stochastic approach to model the observed data by a nonlinearchaotic model disturbed by dynamic noise. In fact, we construct a model havingnegligible or even zero autocorrelations in the conditional mean, but a richstructure in the conditional variance. The model is a noisy Mackey–Glassequation with errors that follow a GARCH(p,q) process. This model permits usto capture volatility-clustering phenomena. Its characteristic is thatvolatility clustering is interpreted as an endogenous phenomenon. The mainobjective of this article is the identification of the underlying process ofthe Paris Stock Exchange returns series CAC40. To this end, we apply severaldifferent tests to detect longmemory components and chaotic structures.Forecasting results for the CAC40 returns series, will conclude this paper.

Mackey–Glass equationnoisy chaosvolatility clusteringcorrelation dimensionLyapunov exponentsGARCH effectsforecasting

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Catherine Kyrtsou
    • 1
  • Michel Terraza
    • 1
  1. 1.Department of Applied Economics, Lameta, Espace RichterUniversity of Montpellier IMontpellier, Cedex 1France