This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be piecewise constant with densities in a H\"{o}lder class. The change points, or times at which the distribution changes, are unknown. We derive the limiting distributions of the change point estimators when the minimal jump size vanishes or remains constant, a first in the literature on change point settings. We are introducing two new features: a consistent estimator that can detect when a change is happening in data with short-term dependence, and a consistent block-type long-run variance estimator. Numerical evidence is provided to back up our theoretical results.

翻译：本文研究多元非参数变点定位与推断问题。数据包含可能存在短期依赖的多元时间序列，其分布被假定为分段常数，且密度函数属于Hölder类。分布发生变化的时刻（即变点）未知。当最小跳跃幅度趋近于零或保持恒定值时，我们推导出变点估计量的极限分布，这在变点设置的相关文献中尚属首次。我们引入两个新方法：一是在短期依赖数据中能检测变点发生的一致性估计量，二是块型长程方差一致性估计量。数值实验为我们的理论结果提供了支持。