In many temporally ordered data sets, it is observed that the parameters of the underlying distribution change abruptly at unknown times. The detection of such changepoints is important for many applications. While this problem has been studied substantially in the linear data setup, not much work has been done for angular data. In this article, we utilize the intrinsic geometry of a torus to introduce the notion of the `square of an angle' and use it to propose a new measure of variation, called the `curved variance', of an angular random variable. Using the above ideas, we propose new tests for the existence of changepoint(s) in the concentration, mean direction, and/or both of these. The limiting distributions of the test statistics are derived and their powers are obtained using extensive simulation. It is seen that the tests have better power than the corresponding existing tests. The proposed methods have been implemented on three real-life data sets revealing interesting insights. In particular, our method when used to detect simultaneous changes in mean direction and concentration for hourly wind direction measurements of the cyclonic storm `Amphan' identified changepoints that could be associated with important meteorological events.

翻译：在许多按时间顺序排列的数据集中，观测到潜在分布的参数会在未知时刻发生突变。此类变点的检测对众多应用具有重要意义。尽管该问题在线性数据场景下已有大量研究，但针对角数据的相关研究仍相对匮乏。本文利用环面的内蕴几何引入"角平方"概念，并据此提出一种新的角随机变量变异性度量——"曲率方差"。基于上述思想，我们提出了新的检验方法，用于检测角数据的浓度、平均方向及其联合变化的变点存在性。推导了检验统计量的极限分布，并通过大量模拟实验评估其检验功效。结果表明，所提检验方法较现有方法具有更优的统计功效。将所提方法应用于三个真实数据集，揭示了有价值的发现。特别地，在检测气旋风暴"安攀"逐时风向测量数据中平均方向与浓度的同步变化时，所提方法识别的变点与重要气象事件存在关联。