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Factor Modeling for High-Dimensional Functional Time Series
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DOI：10.1080/07350015.2025.2505493.png)
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Abstract
En 中文
Many economic and scientific problems involve the analysis of high-dimensional functional time series, where the number of functional variablespdiverges as the number of serially dependent observationsnincreases. In this article, we present a novel functional factor model for high-dimensional functional time series that maintains and makes use of the functional and dynamic structure to achieve great dimension reduction and find the latent factor structure. To estimate the number of functional factors and the factor loadings, we propose a fully functional estimation procedure based on an eigenanalysis for a nonnegative definite and symmetric matrix. Our proposal involves a weight matrix to improve the estimation efficiency and tackle the issue of heterogeneity, the rationale of which is illustrated by formulating the estimation from a novel regression perspective. Asymptotic properties of the proposed method are studied whenpdiverges at some polynomial rate asnincreases. To provide a parsimonious model and enhance interpretability for near-zero factor loadings, we impose sparsity assumptions on the factor loading space and then develop a regularized estimation procedure with theoretical guarantees whenpgrows exponentially fast relative ton. Finally, we demonstrate the superiority of our proposed estimators over the alternatives/competitors through simulations and applications to a U.K. temperature dataset and a Japanese mortality dataset.
Keywords:
Dimension reduction
Functional time series
Functional thresholding
High-dimensional data
Sparse principal component analysis
Journal
J
IF:
2.5
Papers:
96
Citations:
9.1K
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