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

Tinbergen Institute Discussion Paper 16-082/III

34 Pages Posted: 7 Oct 2016

See all articles by Francisco Blasques

Francisco Blasques

VU University Amsterdam; Tinbergen Institute

Paolo Gorgi

University of Padua; VU University Amsterdam - Faculty of Economics and Business Administration

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics; Tinbergen Institute; Aarhus University - CREATES

Olivier Wintenberger

University of Copenhagen; Université Paris VI Pierre et Marie Curie

Date Written: October 4, 2016

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.

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

JEL Classification: C13, C32, C58

Suggested Citation

Blasques, Francisco and Blasques, Francisco and Gorgi, Paolo and Gorgi, Paolo and Koopman, Siem Jan and Wintenberger, Olivier, Feasible Invertibility Conditions and Maximum Likelihood Estimation for Observation-Driven Models (October 4, 2016). Tinbergen Institute Discussion Paper 16-082/III, Available at SSRN: https://ssrn.com/abstract=2848819 or http://dx.doi.org/10.2139/ssrn.2848819

Francisco Blasques (Contact Author)

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Paolo Gorgi

VU University Amsterdam - Faculty of Economics and Business Administration ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

University of Padua ( email )

Via 8 Febbraio, 2
Padova, Vicenza 35122
Italy

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31205986019 (Phone)

HOME PAGE: http://sjkoopman.net

Tinbergen Institute ( email )

Gustav Mahlerplein 117
1082 MS Amsterdam
Netherlands

HOME PAGE: http://personal.vu.nl/s.j.koopman

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Olivier Wintenberger

University of Copenhagen ( email )

Nørregade 10
Copenhagen, København DK-1165
Denmark

Université Paris VI Pierre et Marie Curie

4 place jussieu
Paris, 75005
France

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