Feasible Invertibility Conditions for Maximum Likelihood Estimation for   Observation-Driven Models
  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. 
F Blasques, P Gorgi, S Koopman (CREATES), O Wintenberger (University   of Copenhagen, LSTA)
q-fin.ST math.ST stat.TH