Testing for unit roots in the possible presence of multiple trend breaks using minimum Dickey-Fuller statistics
Testing for unit roots in the possible presence of multiple trend breaks using minimum Dickey-Fuller statistics
复制标题
使用最小迪基富勒统计量测试可能存在多个趋势突破的单位根
DOI：
10.1016/j.jeconom.2013.04.012
复制
发表时间：
2013
影响因子：
6.3
通讯作者：
Harvey D
中科院分区：
文献类型：
--
作者：
Harvey D
趋势突变似乎在宏观经济时间序列中很普遍，因此，如果要避免未建模的趋势突变对功率的严重影响，单位根检验需要考虑这些因素。Carrion-i-Silvestre等人（2009）提出了一种基于预测试的方法，该方法在不发生突变和发生多个突变时都提供了接近渐近有效的单位根推断，前提是突变幅度是固定的。然而，不幸的是，固定幅度的趋势突变渐近理论不能很好地预测这些测试的有限样本功率函数，并且功率对于通常在实践中观察到的趋势突变的幅度可能非常低。针对这个问题，我们提出了一个单位根测试，允许多个中断的趋势，通过采取的序列（在所有候选人的断点在修剪范围内）的下确界的本地GLS去趋势增广Dickey-Fuller型统计。我们表明，这个过程的权力，是强大的任何趋势突破的幅度，从而保持良好的有限样本的力量，在存在的大小不一的突破。我们还证明了，与Zipper和Andrews（1992）的OLS去趋势下确界检验不同，当单位根零点下发生固定幅度趋势突变时，这些检验没有显示出在极限中虚假拒绝的趋势。
Trend breaks appear to be prevalent in macroeconomic time series, and unit root tests therefore need to make allowance for these if they are to avoid the serious effects that unmodelled trend breaks have on power. Carrion-i-Silvestre et al. (2009) propose a pre-test-based approach which delivers near asymptotically efficient unit root inference both when breaks do not occur and where multiple breaks occur, provided the break magnitudes are fixed. Unfortunately, however, the fixed magnitude trend break asymptotic theory does not predict well the finite sample power functions of these tests, and power can be very low for the magnitudes of trend breaks typically observed in practice. In response to this problem we propose a unit root test that allows for multiple breaks in trend, obtained by taking the infimum of the sequence (across all candidate break points in a trimmed range) of local GLS detrended augmented Dickey–Fuller-type statistics. We show that this procedure has power that is robust to the magnitude of any trend breaks, thereby retaining good finite sample power in the presence of plausibly-sized breaks. We also demonstrate that, unlike the OLS detrended infimum tests of Zivot and Andrews (1992), these tests display no tendency to spuriously reject in the limit when fixed magnitude trend breaks occur under the unit root null.