François Roueff (Telecom ParisTech), 18 janvier 2019

vendredi 18 janvier 2019

Résumé : The class of observation-driven models (ODM) includes many model of non-linear time series which, in a fashion similar to, yet different from, hidden Markov models (HMM), involve hidden variables. Interestingly, in contrast to most HMM’€™s, ODM’s enjoy likelihoods that can be computed exactly with computational complexity of the same order as the number of observations, making maximum likelihood estimation the privileged approach for statistical inference for these models. A celebrated example of general order ODM is the GARCH(p, q) model, whose properties have been studied extensively, including ergodicity, likelihood inference or tail behavior. However little is known on more general models, in particular integer-valued ones, such as the log-linear Poisson GARCH or the NBIN-GARCH of order (p, q) about which most of the existing results seem restricted to the case p = q = 1. Here we fill this gap and derive identifiability and ergodicity conditions for general ODM‒s. The consistency and the asymptotic normality of the maximum likelihood estimator can then be derived using methods already developed for first order ODM€’s.