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Asynchronous Changepoint Estimation for Spatially Correlated Functional Time Series.

Mengchen Wang¹, Trevor Harris², Bo Li¹

¹Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL 61820 USA.

Journal of Agricultural, Biological, and Environmental Statistics

|October 24, 2022

Summary

This study introduces a novel Bayesian method for detecting changepoints in spatially correlated functional time series data. The approach improves estimation accuracy and uncertainty quantification by modeling changepoints as a spatial process.

Keywords:

Bayesian hierarchical model Changepoint Functional data Piecewise linear model Spatial correlation

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Area of Science:

Statistics
Time Series Analysis
Spatial Statistics

Background:

Existing methods for functional time series changepoint detection often assume homogeneity or ignore spatial correlations.
This limitation hinders accurate estimation in spatially heterogeneous data.

Purpose of the Study:

To develop a Bayesian framework for simultaneously estimating mean-based asynchronous changepoints in spatially correlated functional time series.
To improve changepoint estimation by incorporating spatial processes and correlations.

Main Methods:

The proposed method utilizes a Bayesian framework and extends the cumulative sum (CUSUM) statistic.
It models changepoints as a spatial process using spatially correlated two-piece linear models with appropriate variance structures.
This approach allows for simultaneous detection of all changepoints, respecting spatial heterogeneity.

Main Results:

Extensive simulations show superior performance compared to existing methods in both estimation accuracy and uncertainty quantification.
The method is robust to weak or strong spatial correlations and change signals.
Improved changepoint estimation, especially near data edges, is achieved.

Conclusions:

The proposed Bayesian spatial approach offers a significant advancement in analyzing functional time series with spatial dependencies.
It provides a more accurate and reliable tool for changepoint detection in various applications, including environmental and epidemiological studies.