Testing for Unit Roots and Non‐linear Transformations
Testing for Unit Roots and Non‐linear Transformations
复制标题
单位根和非线性变换的测试
DOI：
10.1111/1467-9892.00083
复制
发表时间：
1998
影响因子：
0.9
通讯作者：
M. McAleer
中科院分区：
文献类型：
--
作者：
P. Franses;M. McAleer
众所周知，单变量时间序列单位根的增广Dickey-Fuller(ADF)检验对非线性变换很敏感：一个常见的例子是，用对数表示的变量被发现是平稳的，而水平上的相同变量被发现是非平稳的。本文在Box-Cox模型的范围内研究了非线性变换对ADF辅助回归的影响，并建立了一个非线性变换检验来评价ADF回归的充分性。建议的检验计算简单，计算为ADF回归中一个附加变量的t比。本文还分析了具有非线性变换的序列之间的协整关系，并给出了一个检验协整分析中所用的非线性变换的简单方法。Nelson-Plosser数据集中的几个经验例子说明了所提出的单变量序列检验的实际意义，第二个经验例子被用来说明协整序列的非线性变换的检验
It is well known that the augmented Dickey–Fuller (ADF) test of unit roots in univariate time series is sensitive to non‐linear transformations: a common example is when variables expressed in logarithms are found to be stationary, whereas the same variables in levels are found to be non‐stationary. In this paper, the effects of non‐linear transformations on the ADF auxiliary regression are investigated within the class of the Box–Cox model, and a test of non‐linear transformation is developed to assess the adequacy of the ADF regression. The proposed test is computationally simple and is calculated as thet ratio of an added variable in the ADF regression. Cointegration among series which are subject to non‐linear transformations is also analysed, and a simple procedure is developed to test the non‐linear transformation used in cointegration analysis. Several empirical examples taken from the Nelson–Plosser data set illustrate the practical relevance of the proposed test for univariate series, and a second empirical example is used to illustrate the test of non‐linear transformation for cointegrated series