Recursive Adjustment for General Deterministic Components and Improved Cointegration Rank Tests
Recursive Adjustment for General Deterministic Components and Improved Cointegration Rank Tests
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一般确定性成分的递归调整和改进的协整秩检验
DOI：
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发表时间：
2015
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通讯作者：
M. Demetrescu
中科院分区：
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作者：
Benjamin Born;M. Demetrescu
摘要本文讨论了当序列被确定性成分递归调整时，整合向量自回归协整秩的检验问题。为此，递归的渐近性质，或自适应，一般添加剂确定性成分的去除程序进行了分析，在两个不同的，互补的情况下。当随机成分的检查时间序列是弱平稳（如将是平衡误差），递归调整的效果消失，随着样本容量的增加。当适当规范化的随机成分弱收敛到一些具有可积路径的极限连续时间过程时（就像常见的随机趋势的情况一样），递归调整甚至渐近地具有永久的效果：规范化的递归调整过程弱收敛到极限过程的递归调整版本。协整秩检验的零极限分布可以用递归调整的布朗运动表示。此外，有限样本性质的协整秩检验与递归调整的实证相关性的情况下，检查：所考虑的确定性成分是一个常数，一个常数和线性趋势，分别。与似然比检验或广义最小二乘调整的检验相比，在有限样本中发现了空值下经验拒绝频率的改进;在替代方案下也发现了改进，随着初始条件的增加，似然比检验的表现越来越好。关于等级选择，三个测试程序与不同调整的非常简单的组合表现最好。
Abstract This paper discusses tests for the cointegration rank of integrated vector autoregressions when the series are recursively adjusted for deterministic components. To this end, the asymptotic properties of recursive, or adaptive, procedures for the removal of general additive deterministic components are analyzed in two different, complementary, situations. When the stochastic component of the examined time series is weakly stationary (as would be the equilibrium errors), the effect of recursive adjustment vanishes with increasing sample size. When the suitably normalized stochastic component converges weakly to some limiting continuous-time process with integrable paths (as would be the case with the common stochastic trends), recursive adjustment has a permanent effect even asymptotically: the normalized recursively adjusted process converges weakly to a recursively adjusted version of the limiting process. The null limiting distributions of the cointegration rank tests can be expressed in terms of recursively adjusted Brownian motions. Moreover, the finite-sample properties of the cointegration rank tests with recursive adjustment are examined in cases of empirical relevance: the considered deterministic components are a constant, and a constant and a linear trend, respectively. Compared to the likelihood ratio tests or the tests with generalized least squares adjustment, improvements in terms of empirical rejection frequencies under the null are found in finite samples; improvements are found under the alternative as well, with the likelihood ratio test performing increasingly better as the magnitude of the initial condition increases. Regarding rank selection, a very simple combination of the three testing procedures with different adjustments performs best.