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

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Abstract

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 (Computat Econ 21:257–276, 2003) and generalized by Kyrtsou (Int J Bifurcat Chaos 15(10):3391–3394, 2005). To unveil 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 (J Time Ser Anal 4:221–238, 1983), the Brock et al. (Econom Rev 15:197–235, 1996) and Dechert (An application of chaos theory to stochastic and deterministic observations. Working paper, University of Houston, 1995) tests, the correlation-dimension method of Grassberger and Procaccia (Phys 9D:189–208, 1983), the Lyapunov exponents method of Gençay and Dechert (Phys D 59:142–157, 1992), and the Recurrence quantification analysis introduced by Webber and Zbilut (J Appl Physiol 76:965–973, 1994). As a confirmation procedure of the dynamics generating future movements in CAC40, we perform forecast with the use of 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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Authors and Affiliations

  1. Department of Economics, University of Macedonia, Egnatia str., 156, 54006, Thessaloniki, Greece

    Catherine Kyrtsou

  2. Department of Economics, LAMETA, University of Montpellier I, Espace Richter, Avenue de la Mer, 34054, Montpellier Cedex 1, France

    Michel Terraza

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  1. Catherine Kyrtsou
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  2. Michel Terraza
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Correspondence to Catherine Kyrtsou.

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Kyrtsou, C., Terraza, M. Seasonal Mackey–Glass–GARCH process and short-term dynamics. Empir Econ 38, 325–345 (2010). https://doi.org/10.1007/s00181-009-0268-8

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  • DOI: https://doi.org/10.1007/s00181-009-0268-8

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