论文标题
高维量的协整测试的渐近学（$ k $）
Asymptotics of Cointegration Tests for High-Dimensional VAR($k$)
论文作者
论文摘要
论文研究订单$ k $，var（$ k $）的非平稳高维矢量自动化。允许其他确定性术语，例如趋势或季节性。假定的时间段，$ t $和坐标数为$ n $，被假定为较大且订单相同。在这种制度下，得出了Johansen似然比（LR），Pillai-Bartlett和HotellingLawley测试的一阶渐近学：得出：测试统计量会收敛于非随机积分。对于更精致的分析，本文提出并分析了约翰逊测试的修改。缺乏协整的新测试将收敛于通风$ _1 $点过程的部分总和。支持蒙特卡洛模拟表明，在我们定理中考虑的许多情况下，相同的行为在许多情况下都存在。 该论文介绍了该方法的经验实施，用于分析S $ \＆$ p $ 100 $股票和加密货币的经验实现。后一个示例具有多个协整关系的强烈存在，而前者的结果与无协整的零相一致。
The paper studies nonstationary high-dimensional vector autoregressions of order $k$, VAR($k$). Additional deterministic terms such as trend or seasonality are allowed. The number of time periods, $T$, and the number of coordinates, $N$, are assumed to be large and of the same order. Under this regime the first-order asymptotics of the Johansen likelihood ratio (LR), Pillai-Bartlett, and Hotelling-Lawley tests for cointegration are derived: the test statistics converge to nonrandom integrals. For more refined analysis, the paper proposes and analyzes a modification of the Johansen test. The new test for the absence of cointegration converges to the partial sum of the Airy$_1$ point process. Supporting Monte Carlo simulations indicate that the same behavior persists universally in many situations beyond those considered in our theorems. The paper presents empirical implementations of the approach for the analysis of S$\&$P$100$ stocks and of cryptocurrencies. The latter example has a strong presence of multiple cointegrating relationships, while the results for the former are consistent with the null of no cointegration.
