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.

翻译：我们针对在两个时间索引上观测的数据（变化可能同时发生在两个索引维度，且空间分量可能为高维）开发了变化点恢复方法。此项研究源于气候监测问题——这类问题中常存在长序列数据（例如跨多年（索引2）的逐日观测数据（索引1））。此类数据可能随年际时间尺度演变，同时伴随较短时间尺度内的动态季节变化。我们将其建模为二维网格上具有变点的高维均值过程。在单一变点设定下，我们建立了渐近估计与推断理论，包括所提方法的收敛速率及极限分布。该方法进一步推广至多变点情形。理论结果通过蒙特卡洛模拟得到数值验证。我们将所提方法应用于美国太平洋西北地区的大规模气候数据。