Abstract The problem of testing for the equality of autocovariances of two independent high-dimensional time series is studied. Tests based on the suprema or sums of suitable averages across the dimensions are adapted from the available literature. Another test based on principal component analysis (PCA) is introduced and studied in theory. An extension is also considered to the setting of testing for the equality of autocovariances of two populations, having multiple individual high-dimensional series from the two populations. The proposed methodologies are assessed on simulated data, with the performance of the introduced PCA testing being superior overall. An application using fMRI data from individuals experiencing two different emotional states is provided.

中文翻译：

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高维自协方差的两个样本检验

摘要 研究了两个独立的高维时间序列自协方差相等性的检验问题。基于 suprema 或跨维度的合适平均值之和的测试改编自现有文献。另一种基于主成分分析（PCA）的检验被介绍和理论研究。还考虑了对两个群体的自协方差相等性的测试设置的扩展，具有来自两个群体的多个个体高维序列。所提出的方法是在模拟数据上进行评估的，引入的 PCA 测试的性能总体上是优越的。提供了使用来自经历两种不同情绪状态的个体的 fMRI 数据的应用程序。