arXiv 26 Mar 2021 · Statistics — Methodology · publishedJournal of the American Statistical Association (2022) · 13 citations (OpenAlex)
arXiv:2103.14626 · PDF · DOI · OpenAlex · Extracted main text
This paper proposes a hierarchical approximate-factor approach to analyzing high-dimensional, large-scale heterogeneous time series data using distributed computing. The new method employs a multiple-fold dimension reduction procedure using Principal Component Analysis (PCA) and shows great promises for modeling large-scale data that cannot be stored nor analyzed by a single machine. Each computer at the basic level performs a PCA to extract common factors among the time series assigned to it and transfers those factors to one and only one node of the second level. Each 2nd-level computer collects the common factors from its subordinates and performs another PCA to select the 2nd-level common factors. This process is repeated until the central server is reached, which collects common factors from its direct subordinates and performs a final PCA to select the global common factors. The noise terms of the 2nd-level approximate factor model are the unique common factors of the 1st-level clusters. We focus on the case of 2 levels in our theoretical derivations, but the idea can easily be generalized to any finite number of hierarchies. We discuss some clustering methods when the group memberships are unknown and introduce a new diffusion index approach to forecasting. We further extend the analysis to unit-root nonstationary time series. Asymptotic properties of the proposed method are derived for the diverging dimension of the data in each computing unit and the sample size $T$. We use both simulated data and real examples to assess the performance of the proposed method in finite samples, and compare our method with the commonly used ones in the literature concerning the forecastability of extracted factors.
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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 | Lam, C. and Yao, Q (2012) Factor modeling for high-dimensional time series: inference for the number of factors | 1.000 | 8 | 3 | 100% |
| 2 | Ahn, S. C., and Horenstein, A. R (2013) Eigenvalue ratio test for the number of factors | 1.000 | 5 | 3 | 100% |
| 3 | Bai, J. and Ng, S (2002) Determining the number of factors in approximate factor models | 0.941 | 18 | 5 | 83% |
| 4 | Bai J (2003) Inferential theory for factor models of large dimensions | 0.928 | 5 | 4 | 80% |
| 5 | Gao, Z. and Tsay, R. S (2020) Modeling high-dimensional unit-root time series self | 0.928 | 4 | 3 | 100% |
| 6 | Stock, J. H., and Watson, M. W (2002) Macroeconomic forecasting using diffusion indexes | 0.874 | 10 | 2 | 100% |
| 7 | Fan, J., Wang, D., Wang, K., and Zhu, Z (2019) Distributed estimation of principal eigenspaces | 0.874 | 6 | 2 | 100% |
| 8 | Fan, J., Liao, Y., and Mincheva, M. (2013). Large covariance estimat… Journal of the Royal Statistical Society, Series B, 75(4), 603–680 | 0.830 | 7 | 3 | 57% |
| 9 | Alonso, A. M., Galeano, P., and Peña, D (2020) A robust procedure to build dynamic factor models with cluster structure | 0.737 | 3 | 2 | 100% |
| 10 | Gao, Z. and Tsay, R. S (2020) Modeling high-dimensional time series: a factor model with dynamically dependent factors and diverging eigenvalues self | 0.714 | 11 | 3 | 36% |
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