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Feasible Invertibility Conditions for Maximum Likelihood Estimation for Observation-Driven Models

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  • F Blasques

    (CREATES)

  • P Gorgi

    (CREATES)

  • S Koopman

    (CREATES)

  • O Wintenberger

    (University of Copenhagen, LSTA)

Abstract

Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised. We derive considerably weaker conditions that can be used in practice to ensure the consistency of the maximum likelihood estimator for a wide class of observation-driven time series models. Our consistency results hold for both correctly specified and misspecified models. The practical relevance of the theory is highlighted in a set of empirical examples. We further obtain an asymptotic test and confidence bounds for the unfeasible " true " invertibility region of the parameter space.

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  • F Blasques & P Gorgi & S Koopman & O Wintenberger, 2016. "Feasible Invertibility Conditions for Maximum Likelihood Estimation for Observation-Driven Models," Papers 1610.02863, arXiv.org.
    • Handle: RePEc:arx:papers:1610.02863
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    Cited by:

    1. Darolles, Serge & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," Journal of Econometrics, Elsevier, vol. 204(2), pages 223-247.
    2. Christian M. Hafner & Dimitra Kyriakopoulou, 2021. "Exponential-Type GARCH Models With Linear-in-Variance Risk Premium," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 589-603, March.
    3. Vladimír Holý & Jan Zouhar, 2022. "Modelling time‐varying rankings with autoregressive and score‐driven dynamics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1427-1450, November.
    4. Francisco Blasques & Siem Jan Koopman & Gabriele Mingoli, 2023. "Observation-Driven filters for Time- Series with Stochastic Trends and Mixed Causal Non-Causal Dynamics," Tinbergen Institute Discussion Papers 23-065/III, Tinbergen Institute, revised 01 Mar 2024.
    5. Blasques, F. & Gorgi, P. & Koopman, S.J., 2021. "Missing observations in observation-driven time series models," Journal of Econometrics, Elsevier, vol. 221(2), pages 542-568.

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