Bayesian Changepoint Estimation for Spatially Indexed Functional Time Series

Abstract: We propose a Bayesian hierarchical model to simultaneously estimate mean based changepoints in spatially correlated functional time series. Unlike previous methods that assume a shared changepoint at all spatial locations or ignore spatial correlation, our method treats changepoints as a spatial process. This allows our model to respect spatial heterogeneity and exploit spatial correlations to improve estimation. Our method is derived from the ubiquitous cumulative sum (CUSUM) statistic that dominates changepoint detection in functional time series. However, instead of directly searching for the maximum of the CUSUM based processes, we build spatially correlated two-piece linear models with appropriate variance structure to locate all changepoints at once. The proposed linear model approach increases the robustness of our method to variability in the CUSUM process, which, combined with our spatial correlation model, improves changepoint estimation near the edges. We demonstrate through extensive simulation studies that our method outperforms existing functional changepoint estimators in terms of both estimation accuracy and uncertainty quantification, under either weak and strong spatial correlation, and weak and strong change signals. Finally, we demonstrate our method using a temperature data set and a coronavirus disease 2019 (COVID-19) study.