A CENTRAL LIMIT THEOREM FOR MIXING TRIANGULAR ARRAYS OF VARIABLES WHOSE DEPENDENCE IS ALLOWED TO GROW WITH THE SAMPLE SIZE

Christian Francq () and Jean-Michel Zakoïan
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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
Jean-Michel Zakoïan: LFA - Laboratoire de Finance Assurance - Centre de Recherche en Économie et Statistique (CREST) - GENES - Groupe des Écoles Nationales d'Économie et Statistique, EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie - Université de Lille, Sciences et Technologies - Université de Lille, Sciences Humaines et Sociales - PRES Université Lille Nord de France - Université de Lille, Droit et Santé

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Abstract: Conditions ensuring a central limit theorem for strongly mixing triangular arrays are given. Larger samples can show longer range dependence than shorter samples. The result is obtained by constraining the rate growth of dependence as a function of the sample size, with the usual trade-off of memory and moment conditions. An application to heteroskedasticity and autocorrelation consistent estimators is proposed.

Date: 2005-09-23
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Published in Econometric Theory, 2005, 21 (6), pp.1165-1171. ⟨10.1017/S0266466605050577⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05431370

DOI: 10.1017/S0266466605050577

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