Sparse Asymptotic PCA: Identifying Sparse Latent Factors Across Time Horizon

• URL: http://arxiv.org/abs/2407.09738v2
• Date: Tue, 21 Jan 2025 12:18:29 GMT
• Title: Sparse Asymptotic PCA: Identifying Sparse Latent Factors Across Time Horizon
• Authors: Zhaoxing Gao,
• Abstract summary: This paper introduces a novel sparse latent factor modeling framework using sparse Principal Component Analysis ( APCA)<n>Unlike existing methods based on sparse PCA, our approach posits sparsity in the factor processes while allowing non-sparse loadings.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\ell_1$-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 $\ell_0$-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.

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