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A note on integrated periodic GARCH processes

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  • Bibi, Abdelouahab
  • Lescheb, Ines

Abstract

This note examines some probabilistic properties of periodic and integrated periodic generalized autoregressive conditionally heteroskedasticitic ((I)PGARCH) processes. In these models, the parameters are allowed to switch between different regimes and thus constitute an important subclass of switching GARCH process. We show that, similarly to the classical IGARCH processes, a stationary (in periodic sense) solution with infinite variance for the IPGARCH processes may exist.

Suggested Citation

  • Bibi, Abdelouahab & Lescheb, Ines, 2014. "A note on integrated periodic GARCH processes," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 121-124.
    • Handle: RePEc:eee:stapro:v:87:y:2014:i:c:p:121-124
    DOI: 10.1016/j.spl.2014.01.007
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    1. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    2. Bibi, Abdelouahab & Lescheb, Ines, 2010. "Strong consistency and asymptotic normality of least squares estimators for PGARCH and PARMA-PGARCH models," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1532-1542, October.
    3. I. V. Basawa & Robert Lund, 2001. "Large Sample Properties of Parameter Estimates for Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(6), pages 651-663, November.
    4. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
    5. Abdelhakim Aknouche & Abdelouahab Bibi, 2009. "Quasi‐maximum likelihood estimation of periodic GARCH and periodic ARMA‐GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 19-46, January.
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