Spiked eigenvalues of high-dimensional sample autocovariance matrices: CLT and applications
高维样本自协方差矩阵尖峰特征值的中心极限定理及应用
High-dimensional autocovariance matrices play an important role in dimension reduction for high-dimensional time series. In this article, we establish the central limit theorem (CLT) for spiked eigenvalues of high-dimensional sample autocovariance matrices, which are developed under general conditions. The spiked eigenvalues are allowed to go to infinity in a flexible way without restrictions in divergence order. Moreover, the number of spiked eigenvalues and the time lag of…