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Strong consistency and asymptotic normality of least squares estimators for PGARCH and PARMA-PGARCH models

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  • Bibi, Abdelouahab
  • Lescheb, Ines

Abstract

This paper deals with the probabilistic structure and the asymptotic properties of parameters least squares estimates (LSE) for periodic GARCH (PGARCH) and for PARMA-PGARCH models. In this class of models, the parameters are allowed to switch between different regimes. Firstly, we give necessary and sufficient conditions ensuring the existence of stationary solutions (in a periodic sense) and for the existence of moments of any order. Secondly, a least squares estimation approach for estimating PGARCH and PARMA-PGARCH models are discussed. The strong consistency and the asymptotic normality of the estimators are studied given mild regularity conditions, requiring strict stationarity and the finiteness of moments of some order for the errors term.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:19-20:p:1532-1542
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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. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Abdelouahab Bibi & Christian Francq, 2003. "Consistent and asymptotically normal estimators for cyclically time-dependent linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 41-68, March.
    4. 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.
    5. 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.
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    1. Bibi, Abdelouahab & Lescheb, Ines, 2014. "A note on integrated periodic GARCH processes," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 121-124.

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