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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.

Suggested Citation

  • Catherine Kyrtsou & Michel Terraza, 2008. "Seasonal Mackey-Glass-GARCH process and short-term dynamics," Discussion Paper Series 2008_09, Department of Economics, University of Macedonia, revised Sep 2008.
  • Handle: RePEc:mcd:mcddps:2008_09

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    References listed on IDEAS

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    7. 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, Springer;Society for Computational Economics, vol. 21(3), pages 257-276, June.
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    Cited by:

    1. Kyrtsou, Catherine & Malliaris, Anastasios G. & Serletis, Apostolos, 2009. "Energy sector pricing: On the role of neglected nonlinearity," Energy Economics, Elsevier, vol. 31(3), pages 492-502, May.
    2. Nguyen, Dung Tien, 2012. "Mackey–Glass equation driven by fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5465-5472.
    3. Elena Olmedo, 2014. "Forecasting Spanish Unemployment Using Near Neighbour and Neural Net Techniques," Computational Economics, Springer;Society for Computational Economics, vol. 43(2), pages 183-197, February.
    4. Rachida Hennani & Michel Terraza, 2015. "Contributions of a noisy chaotic model to the stressed Value-at-Risk," Economics Bulletin, AccessEcon, vol. 35(2), pages 1262-1273.
    5. Rachida Hennani, 2015. "Can the Lasota(1977)’s model compete with the Mackey-Glass(1977)’s model in nonlinear modelling of financial time series?," Working Papers 15-09, LAMETA, Universtiy of Montpellier, revised Jun 2015.

    More about this item


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

    JEL classification:

    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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