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Locally Optimal Tests against Periodic Autoregression: Parametric and Nonparametric Approaches

Published online by Cambridge University Press:  11 February 2009

Mohamed Bentarzi  and
Marc Hallin
Mohamed Bentarzi
Affiliation:
Université Houari Boumediene
Marc Hallin
Affiliation:
Université Libre de Bruxelles
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Abstract

Locally asymptotically optimal tests are derived for the null hypothesis of traditional AR dependence, with unspecified AR coefficients and unspecified innovation densities, against an alternative of periodically correlated AR dependence. Parametric and nonparametric rank-based versions are proposed. Local powers and asymptotic relative efficiencies (with respect, e.g., to the corresponding Gaussian Lagrange multiplier tests proposed in Ghysels and Hall [1992, “Lagrange Multiplier Tests for Periodic Structures,” unpublished manuscript, CRDE, Montreal] and Liitkepohl [1991, Introduction to Multiple Time Series Analysis, Berlin: Springer-Verlag; 1991, pp. 243–264, in W.E. Griffiths, H. Liitkepohl, & M.E. Block (eds.), Readings in Econometric Theory and Practice, Amsterdam: North-Holland] are computed explicitly; a rank-based test of the van der Waerden type is proposed, for which this ARE is uniformly larger than 1. The main technical tool is Le Cam's local asymptotic normality property.

Type
Research Article
Information
Econometric Theory , Volume 12 , Issue 1 , March 1996 , pp. 88 - 112
Copyright
Copyright © Cambridge University Press 1996

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