# Sparse Asymptotic PCA: Identifying Sparse Latent Factors Across Time Horizon in High-Dimensional Time Series

arXiv: https://arxiv.org/abs/2407.09738 · HTML: https://mlsanity.com/paper/2407.09738/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2024.

## Abstract (arXiv)

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.