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Seasonal Mackey-Glass-GARCH process and short-term dynamics

The aim of this article is the study of complex structures which are behind the short-term predictability of stock returns series. In this regard, we employ a seasonal version of the Mackey-Glass-GARCH(p,q) model, initially proposed by Kyrtsou and Terraza (2003) and generalized by Kyrtsou (2005, 2006). It has either negligible or significant autocorrelations in the conditional mean, and a rich structure in the conditional variance. To reveal short or long memory components and non-linear structures in the French Stock Exchange (CAC40) returns series, we apply the test of Geweke and Porter-Hudak (1983), the Brock et al. (1996) and Dechert (1995) tests, the correlation-dimension method of Grassberger and Procaccia (1983), the Lyapunov exponents method of Gencay and Dechert (1992), and the Recurrence Quantification Analysis introduced by Webber and Zbilut (1994). As a confirmation procedure of the dynamics generating future movements in CAC40, we forecast the return series using a seasonal Mackey-Glass-GARCH(1,1) model. The interest of the forecasting exercise is found in the inclusion of high-dimensional non-linearities in the mean equation of returns.

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Paper provided by Department of Economics, University of Macedonia in its series Discussion Paper Series with number 2008_09.

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Date of creation: Sep 2008
Date of revision: Sep 2008
Handle: RePEc:mcd:mcddps:2008_09
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  1. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-96, July.
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  16. repec:att:wimass:9621 is not listed on IDEAS
  17. Catherine Kyrtsou & Walter C. Labys & Michel Terraza, 2004. "Noisy chaotic dynamics in commodity markets," Empirical Economics, Springer, vol. 29(3), pages 489-502, 09.
  18. Kyrtsou, Catherine & Malliaris, Anastasios G., 2009. "The impact of information signals on market prices when agents have non-linear trading rules," Economic Modelling, Elsevier, vol. 26(1), pages 167-176, January.
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  25. Catherine Kyrtsou & Michel Terraza, 2003. "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," Computational Economics, Society for Computational Economics, vol. 21(3), pages 257-276, June.
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