Maximum-type statistics of certain functions of the sample covariance matrix of high-dimensional vector time series are studied to statistically confirm or reject the null hypothesis that a data set has been collected under normal conditions. The approach generalizes the case of the maximal deviation of the sample autocovariances function from its assumed values. Within a linear time series framework it is shown that Gumbel-type extreme value asymptotics holds true. As applications we discuss long-only mimimal-variance portfolio optimization and subportfolio analysis with respect to idiosyncratic risks, ETF index tracking by sparse tracking portfolios, convolutional deep learners for image analysis and the analysis of array-of-sensors data.

翻译：研究了高维向量时间序列样本协方差矩阵某些函数的最大值型统计量，以在统计上确认或拒绝数据在正常条件下收集的原假设。该方法推广了样本自协方差函数与其假设值最大偏差的情形。在线性时间序列框架下，证明了冈贝尔型极值渐近性成立。作为应用，我们讨论了仅做多最小方差投资组合优化与基于特质风险的子投资组合分析、通过稀疏跟踪投资组合进行的ETF指数跟踪、用于图像分析的卷积深度学习器以及传感器阵列数据分析。