Sparse Asymptotic PCA: Identifying Sparse Latent Factors Across Time Horizon in High-Dimensional Time Series
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909725550968832 |
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| author | Gao, Zhaoxing |
| author_facet | Gao, Zhaoxing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparse Asymptotic PCA: Identifying Sparse Latent Factors Across Time Horizon in High-Dimensional Time Series Gao, Zhaoxing Methodology Econometrics Statistical Finance Machine Learning 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. |
| title | Sparse Asymptotic PCA: Identifying Sparse Latent Factors Across Time Horizon in High-Dimensional Time Series |
| topic | Methodology Econometrics Statistical Finance Machine Learning |
| url | https://arxiv.org/abs/2407.09738 |