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2018 Feasible invertibility conditions and maximum likelihood estimation for observation-driven models
Francisco Blasques, Paolo Gorgi, Siem Jan Koopman, Olivier Wintenberger
Electron. J. Statist. 12(1): 1019-1052 (2018). DOI: 10.1214/18-EJS1416

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.

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Francisco Blasques. Paolo Gorgi. Siem Jan Koopman. Olivier Wintenberger. "Feasible invertibility conditions and maximum likelihood estimation for observation-driven models." Electron. J. Statist. 12 (1) 1019 - 1052, 2018. https://doi.org/10.1214/18-EJS1416

Information

Received: 1 October 2017; Published: 2018
First available in Project Euclid: 15 March 2018

zbMATH: 06864484
MathSciNet: MR3776279
Digital Object Identifier: 10.1214/18-EJS1416

Subjects:
Primary: 62M86
Secondary: 62M20

Keywords: consistency , invertibility , maximum likelihood estimation , observation-driven models , stochastic recurrence equations

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Vol.12 • No. 1 • 2018
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