Chenlei Leng, Degui Li, Hanlin Shang, Yingcun Xia
arXiv 11 Jan 2024 · Econometrics · 3 citations (OpenAlex)
arXiv:2401.05784 · PDF · DOI · OpenAlex · Extracted main text
We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a low-dimensional version (via series approximation) is assumed for the latent functional factors. We extend the classic principal component analysis technique for the estimation of a low-rank structure to the estimation of a large covariance matrix of random functions that satisfies a notion of (approximate) functional "low-rank plus sparse" structure; and generalise the matrix shrinkage method to functional shrinkage in order to estimate the sparse structure of functional idiosyncratic components. Under appropriate regularity conditions, we derive the large sample theory of the developed estimators, including the consistency of the estimated factors and functional factor loadings and the convergence rates of the estimated matrices of covariance functions measured by various (functional) matrix norms. Consistent selection of the number of factors and a data-driven rule to choose the shrinkage parameter are discussed. Simulation and empirical studies are provided to demonstrate the finite-sample performance of the developed model and estimation methodology.
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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 | Fan, Liao \ Mincheva (2013) Large covariance estimation by thresholding principal orthogonal complements (with discussion) | 1.000 | 12 | 4 | 100% |
| 2 | Bai \ Ng (2002) Determining the number of factors in approximate factor models | 1.000 | 8 | 4 | 100% |
| 3 | Fang, Guo \ Qiao (2023) Adaptive functional thresholding for sparse covariance function estimation in high dimensions | 1.000 | 7 | 4 | 100% |
| 4 | Li, Qiao \ Wang (2023) Factor-guided estimation of large covariance matrix function with conditional functional sparsity | 1.000 | 7 | 3 | 100% |
| 5 | Tavakoli, Nisol and Hallin (2023) Factor models for high-dimensional functional time series II: Representation results | 1.000 | 7 | 3 | 100% |
| 6 | Guo, Qiao and Wang (2021) Factor modelling for high-dimensional functional time series | 1.000 | 5 | 3 | 100% |
| 7 | Tavakoli, Nisol and Hallin (2023) Factor models for high-dimensional functional time series II: Estimation and forecasting | 0.935 | 11 | 5 | 82% |
| 8 | Blanchard \ Zadorozhnyi (2019) Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods | 0.737 | 5 | 2 | 60% |
| 9 | Bickel \ Levina (2008) Covariance regularization by thresholding | 0.644 | 2 | 2 | 100% |
| 10 | Kokoszka et al (2018) Dynamic functional regression with application to the cross-section of returns | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 33 scored citations.