# 16-082/III (2016-10-06)

Francisco Blasques, VU University Amsterdam, the Netherlands; Paolo Gorgi, VU University Amsterdam, the Netherlands; University of Padua, Italy; Siem Jan Koopman, VU University Amsterdam, the Netherlands; Aarhus University, Denmark; Olivier Wintenberger, University of Copenhagen, Denmark; Sorbonne Universités, UPMC University Paris 06, France
consistency, invertibility, maximum likelihood estimation, observation-driven models, stochastic recurrence equations
JEL codes:
C13, C32, C58

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.