Estimation du comportement asymptotique des autocovariances et autocorrelations empiriques de processus multivariés

Alain Berlinet and Christian Francq ()
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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] - Groupe ENSAE-ENSAI - 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 - Groupe ENSAE-ENSAI - 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

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Abstract: Abstract Statistics based on the sample autocovariances are widely used in time‐series analysis. Estimators of the asymptotic covariance between the sample autocovariances are commonly derived from the so‐called Bartlett's formula. However, this formula essentially holds for linear processes. This entails that for a wide range of nonlinear time series the above‐mentioned estimators are not suitable. In this paper the behaviour of an alternative estimator is studied within the framework of centered or uncentered multivariate strongly mixing processes. Applications to differential functions of sample autocovariances, such as the sample autocorrelations, are considered.

Date: 2008-12-18
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Published in Canadian Journal of Statistics, 2008, 27 (3), pp.525-546. ⟨10.2307/3316109⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05431291

DOI: 10.2307/3316109

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