|
Abstract:
|
We propose a Bayesian hierarchical model for estimating mean based changepoints in spatially correlated functional time series. Unlike the previous method that assumes a shared changepoint at all spatial locations, our model allows for spatially varying changepoints to respect spatial heterogeneity, and meantime takes spatial correlation into account to facilitate the changepoint estimation. Our method is developed based on the cumulative sum (CUSUM) statistic that has been dominantly used in changepoint detection in functional sequence data. Instead of directly searching for the maximum of the CUSUM based process, we build two-piece piecewise linear models with appropriate variance structure to estimate changepoints. The Bayesian hierarchical model further enables the piecewise linear models to be spatially correlated and fit jointly over all locations. Simulation studies show that our method outperforms existing functional changepoint estimators in terms of both estimation accuracy and uncertainty quantification, under either weak or strong spatial correlation and weak or strong change signals. Finally, we demonstrate our method using a temperature data set and a COVID-19 study.
|
