TESTING FOR A UNIT ROOT IN THE PRESENCE OF A POSSIBLE BREAK IN TREND
TESTING FOR A UNIT ROOT IN THE PRESENCE OF A POSSIBLE BREAK IN TREND
复制标题
在趋势可能出现突破的情况下测试单位根
DOI：
10.1017/s0266466609990259
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发表时间：
2009
影响因子：
0.8
通讯作者：
Robert J. Taylor
中科院分区：
文献类型：
--
作者：
D. Harris;David I. Harvey;S. Leybourne;A. Taylor;Robert J. Taylor
我们考虑在序列中的未知点可能存在线性确定性趋势中断的情况下测试时间序列的单位根的问题。我们提出了一种新的突破分数估计器，当趋势发生突破时，它与速率 Op(T−1) 下的真实突破分数是一致的。然而，与其他可用的估计器不同，当没有趋势突破时，我们的估计器以 Op(T−1/2) 速率收敛到零。与包含趋势突破回归器的准差分 (QD) 去趋势单位根检验结合使用，我们表明这些收敛率确保已知的突破分数零临界值渐近有效。与文献中可用的程序不同，即使趋势没有突破（突破分数为零），这一点也成立。这里，趋势突破回归量从确定性组件中删除，然后应用标准 QD 去趋势单位根测试临界值。我们还提出了第二个程序，该程序利用正式的预测试来确定该系列中的趋势突破，仅在预测试拒绝无突破的情况下才包括趋势突破回归量。这两个过程都确保在趋势突破发生（不发生）时，在限制中应用允许（不允许）趋势突破的正确大小（接近）有效的单位根检验。
We consider the issue of testing a time series for a unit root in the possible presence of a break in a linear deterministic trend at an unknown point in the series. We propose a new break fraction estimator which, where a break in trend occurs, is consistent for the true break fraction at rate Op(T−1). Unlike other available estimators, however, when there is no trend break, our estimator converges to zero at rate Op(T−1/2). Used in conjunction with a quasi difference (QD) detrended unit root test that incorporates a trend break regressor, we show that these rates of convergence ensure that known break fraction null critical values are asymptotically valid. Unlike available procedures in the literature, this holds even if there is no break in trend (the break fraction is zero). Here the trend break regressor is dropped from the deterministic component, and standard QD detrended unit root test critical values then apply. We also propose a second procedure that makes use of a formal pretest for a trend break in the series, including a trend break regressor only where the pretest rejects the null of no break. Both procedures ensure that the correctly sized (near-) efficient unit root test that allows (does not allow) for a break in trend is applied in the limit when a trend break does (does not) occur.