arXiv 13 Jul 2024 · Statistics — Methodology
arXiv:2407.09738 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Connor and Korajczyk (1986) Performance measurement with the arbitrage pricing theory: A new framework for analysis | 1.000 | 6 | 3 | 100% |
| 2 | Connor and Korajczyk (1988) Risk and return in an equilibrium APT: Application of a new test methodology | 1.000 | 6 | 3 | 100% |
| 3 | Kristensen (2017) Diffusion indexes with sparse loadings | 1.000 | 6 | 3 | 100% |
| 4 | Bai and Ng (2013) Principal components estimation and identification of static factors | 0.928 | 5 | 3 | 80% |
| 5 | Bai and Ng (2002) Determining the number of factors in approximate factor models | 0.899 | 11 | 5 | 73% |
| 6 | Johnstone and Lu (2009) On consistency and sparsity for principal components analysis in high dimensions | 0.874 | 7 | 2 | 100% |
| 7 | Ma (2013) Sparse principal component analysis and iterative thresholding | 0.874 | 6 | 2 | 100% |
| 8 | Pelger (2020) Understanding Systematic Risk: A High-Frequency Approach | 0.874 | 5 | 2 | 100% |
| 9 | Gao and Tsay (2023) Divide-and-conquer: a distributed hierarchical factor approach to modeling large-scale time series data | 0.843 | 3 | 3 | 100% |
| 10 | Witten et al (2009) A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis | 0.811 | 4 | 2 | 100% |
Showing the top 10 of 57 scored citations.