Change-Points Detection and Support Recovery for Spatially Indexed Functional Data

TL;DR

This paper develops a unified method for detecting change-points and identifying affected regions in high-dimensional, spatially indexed functional data, addressing challenges of spatial dependence and multiple testing.

Contribution

It introduces a novel framework combining weakly separable covariance, functional PCA, and spatial clustering for change-point detection and support recovery in complex spatiotemporal data.

Findings

Effective change-point detection demonstrated in simulations.

Accurate support recovery of affected locations shown in case study.

Method controls false discovery rate without relying on pointwise p-values.

Abstract

Large volumes of spatiotemporal data, characterized by high spatial and temporal variability, may experience structural changes over time. Unlike traditional change-point problems, each sequence in this context consists of function-valued curves observed at multiple spatial locations, with typically only a small subset of locations affected. This paper addresses two key issues: detecting the global change-point and identifying the spatial support set, within a unified framework tailored to spatially indexed functional data. By leveraging a weakly separable cross-covariance structure -- an extension beyond the restrictive assumption of space-time separability -- we incorporate functional principal component analysis into the change-detection methodology, while preserving common temporal features across locations. A kernel-based test statistic is further developed to integrate spatial clustering pattern into the detection process, and its local variant, combined with the estimated change-point, is employed to identify the subset of locations contributing to the mean shifts. To control the false discovery rate in multiple testing, we introduce a functional symmetrized data aggregation approach that does not rely on pointwise p-values and effectively pools spatial information. We establish the asymptotic validity of the proposed change detection and support recovery method under mild regularity conditions. The efficacy of our approach is demonstrated through simulations, with its practical usefulness illustrated in an application to China's precipitation data.