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

TL;DR

This paper derives weaker invertibility conditions ensuring the consistency of maximum likelihood estimators in observation-driven time series models, applicable even under misspecification, with practical empirical validation.

Contribution

It introduces practically applicable, weaker invertibility conditions for MLE consistency in observation-driven models, extending validity to misspecified cases.

Findings

Weaker invertibility conditions guarantee MLE consistency.

The theory applies to both correctly specified and misspecified models.

Empirical examples demonstrate practical relevance.

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.