Necessary and sufficient conditions for the identifiability of observation-driven models

In this contribution we are interested in proving that a given observation-driven model is identifiable. In the case of a GARCH(p, q) model, a simple sufficient condition has been established in [1] for showing the consistency of the quasi-maximum likelihood estimator. It turns out that this condition applies for a much larger class of observation-driven models, that we call the class of linearly observation-driven models. This class includes standard integer valued observation-driven time series, such as the log-linear Poisson GARCH or the NBIN-GARCH models.

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