In this paper, we derive the Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by the vector autoregressive moving average model when the dimension is comparable to the sample size. This result is applied to make inference on the vector autoregressive moving average model. Simulations are conducted to demonstrate the finite sample performance of our inference.

中文翻译：

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VARMA生成的样本协方差矩阵的最大特征值的Tracy-Widom定律

在本文中，我们推导了向量自回归移动平均模型在维度与样本量相当时生成的样本协方差矩阵的最大特征值的 Tracy-Widom 定律。该结果用于对向量自回归移动平均模型进行推断。进行模拟以证明我们推理的有限样本性能。