英文文献：Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models-非线性协整向量误差修正模型的测试和推理
英文文献作者：Dennis Kristensen,Anders Rahbek
英文文献摘要：
In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing for linearity is of particular interest as parameters of non-linear components vanish under the null. To solve the latter type of testing, we use the so-called sup tests, which here requires development of new (uniform) weak convergence results. These results are potentially useful in general for analysis of non-stationary non-linear time series models. Thus the paper provides a full asymptotic theory for estimators as well as standard and non-standard test statistics. The derived asymptotic results prove to be new compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. With respect to testing, this makes implementation of testing involved, and bootstrap versions of the tests are proposed in order to facilitate their usage. The asymptotic results regarding the QML estimators extend results in Kristensen and Rahbek (2010, Journal of Econometrics) where symmetric non-linear error correction considered. A simulation study shows that the fi?nite sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes.

在本文中，我们考虑了一类一般的矢量误差校正模型，它允许非对称和非线性误差校正。我们提供了基于(拟)极大似然(QML)估计和检验的渐近结果。考虑一般的假设检验，其中线性检验是特别有趣的，因为非线性成分的参数消失在零。为了解决后一种类型的测试，我们使用所谓的上测试，这需要开发新的(一致的)弱收敛结果。这些结果在一般非平稳非线性时间序列模型的分析中是潜在的有用的。因此，本文提供了估计量的全渐近理论以及标准和非标准检验统计量。由于估计协整关系的影响，所导出的渐近结果与文献中其他地方发现的结果相比被证明是新的。关于测试，这就涉及到测试的实现，并且为了方便它们的使用，建议了测试的引导版本。关于QML估计量的渐近结果扩展了Kristensen和Rahbek(2010，计量经济学杂志)中的结果，其中考虑了对称非线性误差修正。一项模拟研究表明，fi?在合理的样本容量下，bootstrap测试的样本性能良好，具有良好的尺寸和功率特性。