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Mixture Periodic GARCH Models: Theory and Applications

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  • Saïd Souam

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

  • Faycal Hamdi

Abstract

This paper discusses mixture periodic GARCH (M-PGARCH) models that constitute very flexible class of nonlinear time series models of the conditional variance. It turns out that they are more parsimonious comparatively to high-order MPARCH models. We first provide some probabilistic properties of this class of models. We thus propose an estimation method based on the Expectation-Maximization (EM) algorithm. Finally, we apply this methodology to model the spot rates of the Algerian dinar against euro and U.S. dollar. This empirical analysis shows that M-PGARCH models yield the best performance among the competing models.

Suggested Citation

  • Saïd Souam & Faycal Hamdi, 2018. "Mixture Periodic GARCH Models: Theory and Applications," Post-Print hal-01589209, HAL.
    • Handle: RePEc:hal:journl:hal-01589209
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    1. Chan, W.S. & Wong, C.S. & Chung, A.H.L., 2009. "Modelling Australian interest rate swap spreads by mixture autoregressive conditional heteroscedastic processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2779-2786.
    2. Kai-Li Wang & Christopher Fawson & Christopher B. Barrett & James B. McDonald, 2001. "A flexible parametric GARCH model with an application to exchange rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(4), pages 521-536.
    3. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    4. Irina Bunda, 2007. "The Changing Role of the Exchange Rate in a Globalised Economy," Post-Print halshs-00372820, HAL.
    5. Roberto Cellini & Tiziana Cuccia, 2014. "Seasonal processes in the Euro--US Dollar daily exchange rate," Applied Financial Economics, Taylor & Francis Journals, vol. 24(3), pages 161-174, February.
    6. Dueker, Michael & Neely, Christopher J., 2007. "Can Markov switching models predict excess foreign exchange returns?," Journal of Banking & Finance, Elsevier, vol. 31(2), pages 279-296, February.
    7. Luc Bauwens & Dagfinn Rime & Genaro Sucarrat, 2008. "Exchange rate volatility and the mixture of distribution hypothesis," Studies in Empirical Economics, in: Luc Bauwens & Winfried Pohlmeier & David Veredas (ed.), High Frequency Financial Econometrics, pages 7-29, Springer.
    8. Kumar, Satish, 2016. "Revisiting calendar anomalies: Three decades of multicurrency evidence," Journal of Economics and Business, Elsevier, vol. 86(C), pages 16-32.
    9. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    10. Philip Hans Franses & Richard Paap, 2000. "Modelling day-of-the-week seasonality in the S&P 500 index," Applied Financial Economics, Taylor & Francis Journals, vol. 10(5), pages 483-488.
    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. Shao, Q., 2006. "Mixture periodic autoregressive time series models," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 609-618, March.
    13. Francq, Christian & ZakoI¨an, Jean-Michel, 2005. "The L2-structures of standard and switching-regime GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1557-1582, September.
    14. Markus Haas, 2004. "Mixed Normal Conditional Heteroskedasticity," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 211-250.
    15. Rim Khemiri, 2012. "Volume and volatility in foreign exchange market microstructure: a Markov switching approach," Applied Financial Economics, Taylor & Francis Journals, vol. 22(14), pages 1121-1133, July.
    16. Aknouche, Abdelhakim & Bentarzi, Mohamed, 2008. "On the existence of higher-order moments of periodic GARCH models," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3262-3268, December.
    17. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

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    2. Bibi, Abdelouahab & Ghezal, Ahmed, 2017. "Asymptotic properties of QMLE for periodic asymmetric strong and semi-strong GARCH models," MPRA Paper 81126, University Library of Munich, Germany.

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