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摘要翻译：
自从Elliott(1998)以来，当自回归根接近但不完全等于统一时，有效的协整关系推理方法就会崩溃。本文在具有非单位根的VAR的框架内解决了这个问题。基于VAR所隐含的脉冲响应函数，我们提出了协整的一个特征，即使根不完全是一个，它仍然是有意义的。在此特征下，用与VaR最大特征根相关联的子空间来识别序列之间的长期平衡关系。我们分析了该子空间的极大似然估计的渐近性，从而推广了Johansen(1995)对具有精确单位根的协整VAR的处理。推论因与预测回归中遇到的类似的麻烦参数问题而变得复杂，可以通过从该环境中熟悉的方法来处理。
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英文标题：
《The Cointegrated VAR without Unit Roots: Representation Theory and
Asymptotics》
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作者：
James A. Duffy and Jerome R. Simons
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最新提交年份：
2020
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分类信息：
一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
It has been known since Elliott (1998) that efficient methods of inference on cointegrating relationships break down when autoregressive roots are near but not exactly equal to unity. This paper addresses this problem within the framework of a VAR with non-unit roots. We develop a characterisation of cointegration, based on the impulse response function implied by the VAR, that remains meaningful even when roots are not exactly unity. Under this characterisation, the long-run equilibrium relationships between the series are identified with a subspace associated to the largest characteristic roots of the VAR. We analyse the asymptotics of maximum likelihood estimators of this subspace, thereby generalising Johansen's (1995) treatment of the cointegrated VAR with exactly unit roots. Inference is complicated by nuisance parameter problems similar to those encountered in the context of predictive regressions, and can be dealt with by approaches familiar from that setting.
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PDF链接：
https://arxiv.org/pdf/2002.08092
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