2024/07/13 by Gao, Zhaoxing
#Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistical Finance (q-fin.ST)
paper · doi:10.48550/arxiv.2407.09738
This paper introduces a novel sparse latent factor modeling framework using sparse asymptotic Principal Component Analysis (APCA) to analyze the co-movements of high-dimensional panel data over time. Unlike existing methods based on sparse PCA, which assume sparsity in the loading matrices, our 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. Unlike the commonly used ℓ1-relaxation in sparse PCA, 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 ℓ0-constraints. Furthermore, we develop a data-driven approach to identify the sparsity of risk factors over the time horizon using a novel cross-sectional cross-validation method. We establish the consistency of our estimators under mild conditions 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, we apply our method to daily S&P 500 stock returns (2004--2016) and identify nine risk factors influencing the stock market.