Feasible Invertibility Conditions and Maximum Likelihood Estimation for Observation-Driven Models
Tinbergen Institute Discussion Paper 16-082/III
34 Pages Posted: 7 Oct 2016
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: Suggested Citation