Cointegration in large VARs
Cointegration in large VARs
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DOI：
10.1214/21-aos2164
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发表时间：
2020-06
期刊：
影响因子：
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通讯作者：
A. Bykhovskaya;V. Gorin
中科院分区：
文献类型：
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作者：
A. Bykhovskaya;V. Gorin
本文分析了向量自回归过程（VAR）中的协整问题，即当坐标数N和时间周期数T都很大且为同阶时，VAR的协整问题。我们提出了一种方法来检查VAR协整的存在的基础上修改的Johansen似然比检验。我们的程序的优势，原来的约翰森测试和它的有限样本校正是，我们的测试不会遭受过度拒绝。这是通过新的渐近定理矩阵的特征值的检验统计量的制度成比例增长$N$和$T$。我们的理论研究结果支持Monte Carlo模拟和实证说明。此外，我们发现了一个令人惊讶的连接与多变量方差分析（MANOVA），并解释了为什么它出现。
The paper analyses cointegration in vector autoregressive processes (VARs) for the cases when both the number of coordinates, $N$, and the number of time periods, $T$, are large and of the same order. We propose a way to examine a VAR for the presence of cointegration based on a modification of the Johansen likelihood ratio test. The advantage of our procedure over the original Johansen test and its finite sample corrections is that our test does not suffer from over-rejection. This is achieved through novel asymptotic theorems for eigenvalues of matrices in the test statistic in the regime of proportionally growing $N$ and $T$. Our theoretical findings are supported by Monte Carlo simulations and an empirical illustration. Moreover, we find a surprising connection with multivariate analysis of variance (MANOVA) and explain why it emerges.