Testing for stationarity with a break
Testing for stationarity with a break
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DOI：
10.1016/s0304-4076(01)00106-3
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发表时间：
2002-05
影响因子：
6.3
通讯作者：
Eiji Kurozumi
中科院分区：
文献类型：
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作者：
Eiji Kurozumi
本文研究了对单位根有结构变化的趋势平稳性的零假设检验。给出了局部备选序列下拉格朗日乘子检验统计量的极限分布及其特征函数。LM检验的局部极限功率取决于过程的平稳分量的持续性，且过程的持续性越强，检验统计量的作用越小。我们还提出了一种检验统计量，它不依赖于零假设下预断点占样本大小的比例，我们称之为PS检验。虽然临界点不依赖于断点是方便的，但在接近零假设的备选方案下，PS检验被发现没有LM检验那么强大。有限样本模拟表明，当突变点已知时，当过程相当持续时，LM检验倾向于过大，而PS检验的尺寸失真不那么明显。另一方面，当用最小二乘法估计折点时，两种检验的经验规模都接近名义规模，但与已知的折点情况相比，其威力有所降低。
In this paper, we investigate a test for the null hypothesis of trend stationarity with a structural change against a unit root. We derive the limiting distribution of an Lagrange Multiplier (LM) test statistic and its characteristic function under a sequence of local alternatives. The local limiting power of the LM test depends on the persistence of the stationary component of the process, and the more persistent the process, the less powerful is the test statistic. We also propose a test statistic that does not depend on the fraction of the pre-break points to the sample size under the null hypothesis, which we call the PS test. Though it is convenient for the critical point not to depend on the break point, the PS test is found to be less powerful than the LM test under the alternative close to the null hypothesis. Finite sample simulations show that when the break point is known, the LM test tends to be oversized when the process is rather persistent, while the size distortion of the PS test is not so pronounced. On the other hand, the empirical sizes of both tests are close to the nominal one when the break point is estimated by the least-squares method, though the power decreases compared with the known break point case.