GENERAL SPATIO-TEMPORAL FACTOR MODELS FOR HIGH-DIMENSIONAL RANDOM FIELDS ON A LATTICE

• 成果类型: Article
• 署名作者: Barigozzi, Matteo; LA Vecchia, Davide; Liu, Hang
• 署名单位: Institut Polytechnique de Paris; ENSAE Paris; University of Geneva; Chinese Academy of Sciences; University of Science & Technology of China, CAS
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2466
• 发表日期: 2025
• 页码: 268-294
• 关键词: dynamic-factor model; time-series; number; covariance

摘要

Motivated by the need for analysing large spatio-temporal panel data, we introduce a novel nonparametric methodology for n-dimensional random fields observed across S spatial locations and T time periods. We call it general spatio-temporal factor model (GSTFM). First, we provide the probabilistic and mathematical underpinning needed for the representation of a random field as the sum of two components: the common component (driven by a small number q of latent factors) and the idiosyncratic component (mildly cross-correlated). We show that the two components are identified as n -> infinity. Second, we propose an estimator of the common component and derive its statistical guarantees (consistency and rate of convergence) as min(n, S, T) -> infinity. Third, we propose an information criterion to determine the number of factors. Estimation makes use of Fourier analysis in the frequency domain and thus it fully exploits the information on the spatio-temporal covariance structure of the whole panel. Synthetic data examples illustrate the applicability of GSTFM and its advantages over the extant generalized dynamic factor model that ignores the spatial correlations.