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Local Asymptotic Normality of General Conditionally Heteroskedastic and Score-Driven Time-Series Models

Author

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  • Christian Francq

    (CREST and University of Lille, France)

  • Jean-Michel Zakoïan

    (University of Lille and CREST, France)

Abstract

The paper establishes the Local Asymptotic Normality (LAN) property for general conditionally heteroskedastic time series models of multiplicative form, ϵt = σt(θ0)ηt, where the volatility σt(θ0) is a parametric function of {ϵs, s

Suggested Citation

  • Christian Francq & Jean-Michel Zakoïan, 2022. "Local Asymptotic Normality of General Conditionally Heteroskedastic and Score-Driven Time-Series Models," Working Papers 2022-06, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2022-06
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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. 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.
    5. 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.
    6. Royer, Julien, 2021. "Conditional asymmetry in Power ARCH($\infty$) models," MPRA Paper 109118, University Library of Munich, Germany.
    7. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(4), pages 539-569, August.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
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    Cited by:

    1. Francq, Christian & Zakoian, Jean-Michel, 2024. "Finite moments testing in a general class of nonlinear time series models," MPRA Paper 121193, University Library of Munich, Germany.

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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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