On White Noises Driven by Hidden Markov Chains

Christian Francq () and Michel Roussignol
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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
Michel Roussignol: LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées - UPEM - Université Paris-Est Marne-la-Vallée - BEZOUT - Fédération de Recherche Bézout - CNRS - Centre National de la Recherche Scientifique - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche Scientifique

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Abstract: We consider a time series model where the variance of the underlying process depends on the state of a non‐observed Markov chain. Maximum likelihood estimates are shown to be consistent. Estimators with asymptotic Gaussian distribution are proposed. Prediction and identification are also mentioned. This is illustrated by means of real and simulated data sets

Date: 2001-12-26
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Published in Journal of Time Series Analysis, 2001, 18 (6), pp.553-578. ⟨10.1111/1467-9892.00068⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05431304

DOI: 10.1111/1467-9892.00068

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