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高维时间序列的自回归筛自助法AI 解读

This paper proposes a new AR-sieve bootstrap approach to high-dimensional time series. The major challenge of classical bootstrap methods on high-dimensional time series is two-fold: curse of dimensionality and temporal dependence. To address such a difficulty, we utilize factor modeling to reduce dimension and capture temporal dependence simultaneously. A factor-based bootstrap procedure is constructed, which performs an AR-sieve bootstrap on the extracted low-dimensional…

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AI 解读

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…