This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise stationary spatio-temporal process, we consider simultaneous estimation of the number and locations of change-points, and model parameters in each segment. A composite likelihood-based criterion is developed for change-point and parameters estimation. Under the framework of increasing domain asymptotics, theoretical results including consistency and distribution of the estimators are derived under mild conditions. In contrast to classical results in fixed dimensional time series that the localization error of change-point estimator is $O_{p}(1)$, exact recovery of true change-points can be achieved in the spatio-temporal setting. More surprisingly, the consistency of change-point estimation can be achieved without any penalty term in the criterion function. In addition, we further establish consistency of the number and locations of the change-point estimator under the infill asymptotics framework where the time domain is increasing while the spatial sampling domain is fixed. A computationally efficient pruned dynamic programming algorithm is developed for the challenging criterion optimization problem. Extensive simulation studies and an application to U.S. precipitation data are provided to demonstrate the effectiveness and practicality of the proposed method.

翻译：本文针对非平稳时空过程的时间维度，提出了一种统一且计算高效的变点估计方法。通过将非平稳时空过程建模为分段平稳时空过程，我们同时估计变点的个数与位置以及每个分段的模型参数。基于复合似然准则，我们构建了用于变点与参数估计的判据。在递增域渐近框架下，在温和条件下推导了估计量的一致性及分布等理论结果。与固定维时间序列中变点估计定位误差为$O_{p}(1)$的经典结果不同，在时空场景下可实现对真实变点的精确恢复。更令人意外的是，无需在准则函数中引入任何惩罚项即可达成变点估计的一致性。此外，我们进一步在时间域递增而空间采样域固定的填充渐近框架下，建立了变点估计个数与位置的一致性。针对该具有挑战性的准则优化问题，我们开发了一种计算高效的剪枝动态规划算法。通过大量模拟实验及对美国降水数据的应用分析，验证了所提方法的有效性与实用性。