THE LIKELIHOOD RATIO TEST FOR COINTEGRATION RANKS IN THE I(2) MODEL
THE LIKELIHOOD RATIO TEST FOR COINTEGRATION RANKS IN THE I(2) MODEL
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DOI：
10.1017/s0266466607070272
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发表时间：
2007-04
影响因子：
0.8
通讯作者：
Heino Bohn Nielsen;Anders Rahbek
中科院分区：
文献类型：
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作者：
Heino Bohn Nielsen;Anders Rahbek
本文提出了 I(2) 向量自回归模型中协整关系数量的似然比 (LR) 检验。结果表明，协整等级的 LR 检验的渐近分布与基于 Johansen (1995, Econometric Theory 11, 25–59)、Paruolo (1996, Journal of Econometrics 72, 313–356) 以及 Rahbek、Kongsted 和Jørgensen（1999，《计量经济学杂志》90, 265–289）。通过构造，LR 检验统计量小于两步过程中的非 LR 检验统计量，并且 LR 检验的应用可能会改变实证工作中的等级选择。基于对现有经验应用和相关蒙特卡罗模拟的研究，我们得出结论，与基于两步的测试相比，LR 测试具有更好的尺寸属性。总的来说，我们建议在 I(2) 分析中使用 LR 检验来确定等级。非常感谢与 Søren Johansen、Hans Christian Kongsted 和 Bent Nielsen 的讨论。我们还感谢编辑和三位匿名审稿人非常有建设性的评论，这些评论使论文的版本有了很大的改进。这项研究得到了丹麦社会科学研究委员会拨款 2114-04-0001 的支持。
This paper presents the likelihood ratio (LR) test for the number of cointegrating relations in the I(2) vector autoregressive model. It is shown that the asymptotic distribution of the LR test for the cointegration ranks is identical to the asymptotic distribution of the much applied test statistic based on the two-step estimation procedure in Johansen (1995, Econometric Theory 11, 25–59), Paruolo (1996, Journal of Econometrics 72, 313–356), and Rahbek, Kongsted, and Jørgensen (1999, Journal of Econometrics 90, 265–289). By construction the LR test statistic is smaller than the non-LR test statistic from the two-step procedure, and application of the LR test may change rank selection in empirical work. Based on a study of existing empirical applications and related Monte Carlo simulations we conclude that the LR test has much better size properties when compared to the two-step-based test. Overall, we propose use of the LR test for rank determination in I(2) analysis.Discussions with Søren Johansen, Hans Christian Kongsted, and Bent Nielsen are gratefully acknowledged. We also thank the editor and three anonymous referees for very constructive comments that have led to a much improved version of the paper. This research was supported by Danish Social Sciences Research Council grant 2114-04-0001.