Ergodicity of observation-driven time series models and consistency of the maximum likelihood estimator

TL;DR

This paper establishes conditions for stationarity and ergodicity in observation-driven time series models, especially counts, and proves the consistency of maximum likelihood estimators under various model specifications.

Contribution

It provides new theoretical conditions ensuring stationarity and ergodicity, and demonstrates the consistency of MLEs for both well-specified and misspecified models.

Findings

Conditions for strict-sense stationarity established

Ergodicity of observation-driven models proven

MLE consistency shown for various model specifications

Abstract

This paper deals with a general class of observation-driven time series models with a special focus on time series of counts. We provide conditions under which there exist strict-sense stationary and ergodic versions of such processes. The consistency of the maximum likelihood estimators is then derived for well- specified and misspecified models.