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


  • F Blasques


  • P Gorgi


  • S Koopman


  • O Wintenberger

    (University of Copenhagen, LSTA)


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,
  • Handle: RePEc:arx:papers:1610.02863

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    1. Francisco Blasques & Paolo Gorgi & Siem Jan Koopman & Olivier Wintenberger, 2015. "A Note on “Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model”," Tinbergen Institute Discussion Papers 15-131/III, Tinbergen Institute.
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    Cited by:

    1. Darolles, Serges & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," MPRA Paper 83988, University Library of Munich, Germany.

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