Factor Modeling for High-Dimensional Functional Time Series
针对高维函数型时间序列，提出一种函数型因子模型，通过完全函数型的估计方法实现降维和潜在因子提取，并在英国温度数据和日本死亡率数据中验证了优越性。
Many economic and scientific problems involve the analysis of high-dimensional functional time series, where the number of functional variables p diverges as the number of serially dependent observations n increases. 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 when p diverges at some polynomial rate as n increases. 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 when p grows exponentially fast relative to n. 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.