Efficient use of higher‐lag autocorrelations for estimating autoregressive processes

Laurence Broze (), Christian Francq () and Jean‐michel Zakoïan
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Laurence Broze: LPP - Laboratoire Paul Painlevé - UMR 8524 - Université de Lille - CNRS - Centre National de la Recherche Scientifique
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
Jean‐michel Zakoïan: CREST - Centre de Recherche en Economie et Statistique [Bruz] - 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, IP Paris - Institut Polytechnique de Paris

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Abstract: The Yule–Walker estimator is commonly used in time‐series analysis, as a simple way to estimate the coefficients of an autoregressive process. Under strong assumptions on the noise process, this estimator possesses the same asymptotic properties as the Gaussian maximum likelihood estimator. However, when the noise is a weak one, other estimators based on higher‐order empirical autocorrelations can provide substantial efficiency gains. This is illustrated by means of a first‐order autoregressive process with a Markov‐switching white noise. We show how to optimally choose a linear combination of a set of estimators based on empirical autocorrelations. The asymptotic variance of the optimal estimator is derived. Empirical experiments based on simulations show that the new estimator performs well on the illustrative model.

Date: 2002-05-28
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Published in Journal of Time Series Analysis, 2002, 23 (3), pp.287-312. ⟨10.1111/1467-9892.00265⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05431269

DOI: 10.1111/1467-9892.00265

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