In this paper we propose a new method for multiple change-point detection for piecewise-constant circular signals, a setting that, despite its importance in many scientific domains, remains comparatively under-explored. The proposed method, Permutation-based Circular Isolate-Detect, denoted PCID, uses an appropriately chosen contrast function and permutation testing to detect change-points in an offline manner, for the data sequence under consideration. Prior to detection, PCID isolates the change-points. The contrast function used is derived under the assumption of von Mises distribution for the noise, but we show that the method is robust and performs well for other distributions as well. Simulations are used to showcase the usability of the method in different signal and noise structures, including serially correlated noise. In order to exhibit the practical relevance of the method in real-world applications, PCID is applied to three real-world datasets, namely flare, acrophase and wave data.

翻译：本文针对分段恒定环形信号提出了一种新的多变化点检测方法。尽管该设定在许多科学领域中具有重要意义，但目前相关研究仍相对较少。所提出的方法称为基于排列检验的环形隔离检测法，简称PCID，该方法通过精心设计的对比函数和排列检验，以离线方式检测给定数据序列中的变化点。在检测之前，PCID会先对变化点进行隔离处理。对比函数的推导基于噪声服从von Mises分布的假设，但我们证明该方法具有鲁棒性，在其他分布条件下同样表现良好。通过仿真实验展示了该方法在不同信号与噪声结构（包括序列相关噪声）中的适用性。为体现该方法在实际应用中的价值，我们将PCID应用于三个真实数据集：耀斑数据、峰值相位数据和波浪数据。