Asymptotic Relative Efficiency of Goodness‐Of‐Fit Tests Based on Inverse and Ordinary Autocorrelations

Ahmed El Ghini and Christian Francq ()
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Ahmed El Ghini: LIFL - FOX MIIRE - LIFL - Laboratoire d'Informatique Fondamentale de Lille - Université de Lille, Sciences et Technologies - Inria - Institut National de Recherche en Informatique et en Automatique - Université de Lille, Sciences Humaines et Sociales - 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

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Abstract: Abstract. We compare the performance of the inverse and ordinary (partial) autocorrelations for time series model identification. It is found that, both in terms of Bahadur's slope and Pitman's asymptotic relative efficiency, the inverse partial autocorrelations are more efficient than the ordinary autocorrelations for identification of moving‐average models. By duality, the partial autocorrelations turn out to be more powerful than the inverse autocorrelations to identify autoregressive models. Numerical experiments on both simulated and real data sets are presented to highlight the theoretical results.

Date: 2006-06-16
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Published in Journal of Time Series Analysis, 2006, 27 (6), pp.843-855. ⟨10.1111/j.1467-9892.2006.00491.x⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05431363

DOI: 10.1111/j.1467-9892.2006.00491.x

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