ON THE BEHAVIOR OF FIXED-bTREND BREAK TESTS UNDER FRACTIONAL INTEGRATION
研究了当数据冲击可能服从分数阶积分时，固定b趋势断点检验的表现，发现检验临界值依赖于分数阶参数δ，并提出了使用δ自适应临界值来修正尺寸扭曲的方法。
Testing for the presence of a broken linear trend when the nature of the persistence in the data is unknown is not a trivial problem, because the test needs to be both asymptotically correctly sized and consistent, regardless of the order of integration of the data. In a recent paper, Sayginsoy and Vogelsang (2011, Econometric Theory 27, 992–1025) (SV) show that tests based on fixed- b asymptotics provide a useful solution to this problem in the case where the shocks may be either weakly dependent or display strong dependence within the near-unit-root class. In this paper we analyze the performance of these tests when the shocks may be fractionally integrated, an alternative model paradigm that allows for either weak or strong dependence in the shocks. We demonstrate that the fixed- b trend break statistics converge to well-defined limit distributions under both the null and local alternatives in this case (and retain consistency against fixed alternatives), but that these distributions depend on the fractional integration parameter δ . As a result, it is only when δ is either zero or one that the SV critical values yield correctly sized tests. Consequently, we propose a procedure that employs δ -adaptive critical values to remove the size distortions in the SV test. In addition, use of δ -adaptive critical values also allows us to consider a simplification of the SV test that is (asymptotically) correctly sized across δ but can also provide a significant increase in power over the standard SV test when δ = 1.