A0438
Title: Sparse asymptotic PCA: Identifying sparse latent factors across time horizon in high-dimensional time series
Authors: Zhaoxing Gao - University of Electronic Science and Technology of China (China) [presenting]
Abstract: A novel sparse latent factor modeling framework is introduced using sparse asymptotic principal component analysis (APCA) to analyze the co-movements of high-dimensional time series data. Unlike existing methods based on sparse PCA, which assume sparsity in the loading matrices, the approach posits sparsity in the factor processes while allowing non-sparse loadings. This is motivated by the fact that financial returns typically exhibit universal and non-sparse exposure to market factors. The proposed sparse APCA employs a truncated power method to estimate the leading sparse factor and a sequential deflation method for multi-factor cases under $\ell_0$-constraints. Furthermore, a data-driven approach is developed to identify the sparsity of risk factors over the time horizon using a novel cross-sectional cross-validation method. The consistency of the estimators is established under mild conditions for dependent data as both the dimension $N$ and the sample size $T$ grow. Monte Carlo simulations demonstrate that the proposed method performs well in finite samples. Empirically, the method is applied to daily S\&P 500 stock returns from 2004 to 2016. Using textual analysis, specific events linked to the identified sparse factors are investigated, and nine key risk factors that influence the stock market are uncovered.
