Feasible invertibility conditions and maximum likelihood estimation for observation-driven models

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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. We also obtain an asymptotic test and confidence bounds for the unfeasible “true” invertibility region of the parameter space. The practical relevance of the theory is highlighted in a set of empirical examples. For instance, we derive the consistency of the maximum likelihood estimator of the Beta-t-GARCH model under weaker conditions than those considered in previous literature.

Original languageEnglish
Pages (from-to)1019-1052
Number of pages34
JournalElectronic Journal of Statistics
Volume12
Issue number1
Early online date15 Mar 2018
DOIs
Publication statusPublished - Mar 2018

Funding

∗Koopman acknowledges financial support by the Center for Research in Econometric Analysis of Time Series (DNRF78), CREATES, funded by the Danish National Research Foundation. †Financial support by the ANR network AMERISKA ANR 14 CE20 0006 01 is gratefully acknowledged by Olivier Wintenberger.

FundersFunder number
CREATES
Center for Research in Econometric Analysis of Time SeriesDNRF78
Agence Nationale de la Recherche
Danmarks Grundforskningsfond

    Keywords

    • Consistency
    • Invertibility
    • Maximum likelihood estimation
    • Observation-driven models
    • Stochastic recurrence equations

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