Randall Douc: Asymptotic properties of Quasi-Maximum Likelihood Estimators in Observation-Driven Time Series models

We study a general class of quasi-maximum likelihood estimators for observation-driven time series models.
Such models can be found in diverse applications including finance, medicine and several other scientific fields.
Our focus is on models related to the exponential family of distributions like Poisson based models for count time
series or duration models. However the proposed approach is more general and covers a variety of time series
models including the ordinary GARCH model which has been studied extensively in the literature. We
provide general conditions under which quasi-maximum likelihood estimators
can be analyzed for this class of time series models and we prove that these
estimators are consistent and asymptotically normal regardless of the true data
generating process. We illustrate our results using classical examples of quasi-
maximum likelihood estimation including standard GARCH models, duration
models, Poisson type autoregressions and ARMA models with GARCH errors.
Our contribution unifies the existing theory and gives conditions for proving
consistency and asymptotic normality in variety of situations.