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Local asymptotic normality of general conditionally heteroskedastic and score-driven time-series models

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  • Francq, Christian
  • Zakoian, Jean-Michel

Abstract

The paper establishes the Local Asymptotic Normality (LAN) property for general conditionally heteroskedastic time series models of multiplicative form, $\epsilon_t=\sigma_t(\btheta_0)\eta_t$, where the volatility $\sigma_t(\btheta_0)$ is a parametric function of $\{\epsilon_{s}, s

Suggested Citation

  • Francq, Christian & Zakoian, Jean-Michel, 2021. "Local asymptotic normality of general conditionally heteroskedastic and score-driven time-series models," MPRA Paper 106542, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:106542
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    References listed on IDEAS

    as
    1. Swensen, Anders Rygh, 1985. "The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend," Journal of Multivariate Analysis, Elsevier, vol. 16(1), pages 54-70, February.
    2. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024.
    3. Drost, Feike C. & Klaassen, Chris A. J., 1997. "Efficient estimation in semiparametric GARCH models," Journal of Econometrics, Elsevier, vol. 81(1), pages 193-221, November.
    4. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(4), pages 539-569, August.
    5. Bernard Garel & Marc Hallin, 1995. "Local asymptotic normality of multivariate ARMA processes with a linear trend," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 551-579, September.
    6. Zhu, Dongming & Galbraith, John W., 2010. "A generalized asymmetric Student-t distribution with application to financial econometrics," Journal of Econometrics, Elsevier, vol. 157(2), pages 297-305, August.
    7. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1994. "Adaptive estimation in time-series models," Discussion Paper 1994-88, Tilburg University, Center for Economic Research.
    8. Marc Hallin & Masanobu Taniguchi & Abdeslam Serroukh & Kokyo Choy, 1999. "Local asymptotic normality for regression models with long-memory disturbance, with statistical applications," ULB Institutional Repository 2013/2091, ULB -- Universite Libre de Bruxelles.
    9. Drew Creal & Siem Jan Koopman & André Lucas, 2008. "A General Framework for Observation Driven Time-Varying Parameter Models," Tinbergen Institute Discussion Papers 08-108/4, Tinbergen Institute.
    10. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    11. Royer, Julien, 2021. "Conditional asymmetry in Power ARCH($\infty$) models," MPRA Paper 109118, University Library of Munich, Germany.
    12. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(5), pages 818-887, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    APARCH; Asymmetric Student-$t$ distribution; Beta-$t$-GARCH; Conditional heteroskedasticity; LAN in time series; Quadratic mean differentiability.;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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