Poisson QMLE of Count Time Series Models

Ali Ahmad () and Christian Francq ()
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Ali Ahmad: CREATIS - Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - INSERM - Institut National de la Santé et de la Recherche Médicale - CNRS - Centre National de la Recherche Scientifique, Université Lille 3 (EQUIPPE)
Christian Francq: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, IP Paris - Institut Polytechnique de Paris, Université Lille 3 (EQUIPPE)

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Abstract: Regularity conditions are given for the consistency of the Poisson quasi‐maximum likelihood estimator of the conditional mean parameter of a count time series model. The asymptotic distribution of the estimator is studied when the parameter belongs to the interior of the parameter space and when it lies at the boundary. Tests for the significance of the parameters and for constant conditional mean are deduced. Applications to specific integer‐valued autoregressive (INAR) and integer‐valued generalized autoregressive conditional heteroscedasticity (INGARCH) models are considered. Numerical illustrations, Monte Carlo simulations and real data series are provided.

Date: 2015-11-03
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Published in Journal of Time Series Analysis, 2015, 37 (3), pp.291-314. ⟨10.1111/jtsa.12167⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05417334

DOI: 10.1111/jtsa.12167

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