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 and Michel Terraza

Computational Economics, 2003, vol. 21, issue 3, 257-276

Abstract: 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. Copyright Kluwer Academic Publishers 2003

Keywords: Mackey–Glass equation; noisy chaos; volatility clustering; correlation dimension; Lyapunov exponents; GARCH effects; forecasting (search for similar items in EconPapers)
Date: 2003
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (31)

Downloads: (external link)
http://hdl.handle.net/10.1023/A:1023939610962 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:compec:v:21:y:2003:i:3:p:257-276

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/10614/PS2

DOI: 10.1023/A:1023939610962

Access Statistics for this article

Computational Economics is currently edited by Hans Amman

More articles in Computational Economics from Springer, Society for Computational Economics Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().