A FIXED-bPERSPECTIVE ON THE PHILLIPS–PERRON UNIT ROOT TESTS
将固定b渐近理论扩展到非参数菲利普斯-佩龙单位根检验，发现其极限依赖干扰参数，解释了有限样本问题，并提出了修正检验以实现渐近枢轴推断。
In this paper we extend fixed- b asymptotic theory to the nonparametric Phillips–Perron (PP) unit root tests. We show that the fixed- b limits depend on nuisance parameters in a complicated way. These nonpivotal limits provide an alternative theoretical explanation for the well-known finite-sample problems of the PP tests. We also show that the fixed- b limits depend on whether deterministic trends are removed using one-step or two-step detrending approaches. This is in contrast to the asymptotic equivalence of the one- and two-step approaches under a consistency approximation for the long-run variance estimator. Based on these results we introduce modified PP tests that allow for asymptotically pivotal fixed- b inference. The theoretical analysis is cast in the framework of near-integrated processes, which allows us to study the asymptotic behavior both under the unit root null hypothesis and for local alternatives. The performance of the original and modified PP tests is compared by means of local asymptotic power and a small finite-sample simulation study.