LOCALLY OPTIMAL TESTS AGAINST PERIODIC AUTOREGRESSION - PARAMETRIC AND NONPARAMETRIC APPROACHES

Locally asymptotically optimal tests are derived for the null hypothes is of traditional AR dependence, with unspecified AR coefficients and unspecified innovation densities, against an alternative of periodical ly correlated AR dependence. Parametric and nonparametric rank-based v ersions are proposed, Local powers and asymptotic relative efficiencie s (with respect, e.g., to the corresponding Gaussian Lagrange multipli er tests proposed in Ghysels and Hall [1992, ''Lagrange Multiplier Tes ts for Periodic Structures,'' unpublished manuscript, CRDE, Montreal] and Lutkepohl [1991, Introduction to Multiple Time Series Analysis, Be rlin: Springer-Verlag; 1991, pp. 243-264, in W.E. Griffiths, H. Lutkep ohl, & 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 uniform ly larger than 1, The main technical tool is Le Cam's local asymptotic normality property.