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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 (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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Bibliographic Info

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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Web page: http://www.uom.gr/index.php?tmima=3

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Keywords: Noisy chaos; short-term dynamics; correlation dimension; Lyapunov exponents; recurrence quantifications; forecasting.;

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Cited by:
  1. Nguyen, Dung Tien, 2012. "Mackey–Glass equation driven by fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 391(22), pages 5465-5472.
  2. Elena Olmedo, 2014. "Forecasting Spanish Unemployment Using Near Neighbour and Neural Net Techniques," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 43(2), pages 183-197, February.

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