High Dimensional Change Point Models for Two-Directional Data

2026-06-05

AI Summary

This study addresses the challenge of detecting structural changes in high-dimensional data that occur simultaneously at both daily and annual temporal scales. It proposes a unified modeling framework for mean change points on a two-dimensional grid, developing estimation and inference methods applicable to both single and multiple change-point scenarios. By leveraging piecewise constant mean modeling, high-dimensional statistical inference, and asymptotic theory, the work establishes convergence rates and limiting distributions for change-point locations, with theoretical results corroborated through Monte Carlo simulations. The methodology is successfully applied to large-scale climate data from the Pacific Northwest of the United States, effectively identifying joint change patterns across interannual and seasonal scales, thereby substantially enhancing the accuracy and interpretability of change-point detection under dual temporal structures.

Abstract

We develop methodology for recovery of change points for data observed on more than one temporal index where changes may occur simultaneous in both indices, where the spatial component may be high dimensional. The work is motivated by climate monitoring problems where long series of data are available, e.g., daily observations (index 1) over several years (index 2). Such data may be evolving over the annual time scale, along with dynamic seasonal changes in the shorter time scale. We model this as a high dimensional mean process observed on a two dimensional grid with change points. Asymptotic estimation and inference results are developed under a single change point setup, including rates of convergence of the proposed method as well the resulting limiting distributions. The method is extended to the case of multiple changes. Theoretical results are supported numerically with monte-carlo simulations. We implement our work on a large scale climate data for the Pacific Northwest region of the United States.

Problem

• change point detection
• high dimensional data
• two-directional time series
• climate monitoring
• mean process

Innovation

• high-dimensional change point
• two-directional data
• asymptotic inference
• climate monitoring
• multiple change points