Locally Optimal Tests against Periodic Autoregression: Parametric and Nonparametric Approaches

Mohamed Bentarzi and Marc Hallin ()

Econometric Theory, 1996, vol. 12, issue 01, pages 88-112

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(with respect, e.g., to the corresponding Gaussian Lagrange multiplier tests proposed in Ghysels and Hall [1992, unpublished manuscript, CRDE, Montreal] and Liitkepohl [1991, Introduction to Multiple Time Series Analysis, Berlin: Springer-Verlag; 1991, pp. 243 264, in W.E. Griffiths,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.

Date: 1996

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