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Title: Spiked eigenvalues of high-dimensional sample autocovariance matrices: CLT and applications Authors:  Yanrong Yang - The Australian National University (Australia) [presenting]
Han Xiao Han - USTC (China)
Abstract: High-dimensional autocovariance matrices play an important role in dimension reduction for high-dimensional time series. We establish the central limit theorem (CLT) for spiked eigenvalues of high-dimensional sample autocovariance matrices, which is 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 the autocovariance matrix under study could be either fixed or tending to infinity when the dimension p and the time length T go to infinity together. As a further statistical application, a novel autocovariance test is proposed to detect the equivalence of spiked eigenvalues for two high-dimensional time series. Various simulation studies are illustrated to justify the theoretical findings. Furthermore, a hierarchical clustering approach based on the autocovariance test is constructed and applied to clustering mortality data from multiple countries.