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

Randal Douc 1 François Roueff 2, 3, 4 Tepmony Sim 5 
1 TIPIC-SAMOVAR - Traitement de l'Information Pour Images et Communications
SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
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LTCI - Laboratoire Traitement et Communication de l'Information
Abstract : 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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Submitted on : Tuesday, September 8, 2020 - 9:50:23 AM
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Randal Douc, François Roueff, Tepmony Sim. Necessary and sufficient conditions for the identifiability of observation-driven models. Journal of Time Series Analysis, Wiley-Blackwell, 2021, 42 (2), pp.140-160. ⟨10.1111/jtsa.12559⟩. ⟨hal-02088860v3⟩



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