Changepoint detection and estimation for spatially indexed functional time series

Wang, Mengchen

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https://hdl.handle.net/2142/120532 Copy

Description

Title

Changepoint detection and estimation for spatially indexed functional time series

Author(s)

Wang, Mengchen

Issue Date

2023-04-23

Director of Research (if dissertation) or Advisor (if thesis)

• Li, Bo
• Harris, Trevor

Doctoral Committee Chair(s)

Li, Bo

Committee Member(s)

• Shao, Xiaofeng
• Park, Trevor

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Bayesian hierarchical model
• Changepoint
• Functional data
• Spatial correlation

Abstract

We develop mean-based asynchronous changepoints estimation and detection methods for spatially indexed functional time series in the Bayesian framework. Chapter 2 proposes to build spatially correlated two-piece linear models with appropriate variance structure for modeling a process based on the cumulative sum (CUSUM) statistic. The method allows spatially varying changepoints and exploits spatial correlations to improve estimation. We perform comprehensive simulations to explore settings with weak or strong spatial correlation and weak or strong change signals. The results indicate that our method provides better estimation accuracy and uncertainty quantification compared to existing functional changepoint estimators. We demonstrate our method using a temperature data set and a coronavirus disease 2019 study. In Chapter 3, we develop a compact approach by combining detection and estimation in a single Bayesian hierarchical model. We further enhance the estimation accuracy using a quadratic fit and introduce a parameter directly describing the magnitude of the change signal. We employ a continuous spike-and-slab prior with a mixture of two truncated normal distributions for the change magnitude parameter to detect changepoint. Extensive simulations demonstrate that our method works well for various scenarios including data with different proportions of null locations, different strengths of spatial correlations, and different sizes of change signals. We apply our method to analyze the influence of the June 15th, 1991 eruption of Mount Pinatubo on global temperatures. We detect changepoints in a spatially smoothing pattern, where regions at similar latitudes exhibit similar changepoints. The results show evidence of the early impact of the eruption on low-latitude regions, later impact on high latitudes, and little impact on the southern hemisphere.

Graduation Semester

2023-05

Type of Resource

Thesis

Copyright and License Information

Copyright 2023 Mengchen Wang

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