Locally Optimal Tests against Periodic Autoregression: Parametric and Nonparametric Approaches
针对传统AR模型与周期自回归备择假设，推导了局部渐近最优检验，包括参数和基于秩的非参数版本，并计算了局部势和渐近相对效率。
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Lagrange multiplier tests proposed in Ghysels and Hall [1992, “Lagrange Multiplier Tests for Periodic Structures,” unpublished manuscript, CRDE, Montreal] and Liitkepohl [1991, Introduction to Multiple Time Series Analysis, Berlin: Springer-Verlag; 1991, pp. 243–264, in W.E. Griffiths,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.