We consider detection of multiple changes in the distribution of periodic and autocorrelated data with known period. To account for periodicity we transform the sequence of vector observations by arranging them in matrices and thereby producing a sequence of independently and identically distributed matrix observations. We propose methods of testing the equality of matrix distributions and present methods that can be applied to matrix observations using the E‐divisive algorithm. We show that periodicity and autocorrelation degrade existing change detection methods because they blur the changes that these procedures aim to discover. Methods that ignore the periodicity have low power to detect changes in the mean and the variance of periodic time series when the periodic effects overwhelm the true changes, while the proposed methods detect such changes with high power. We illustrate the proposed methods by detecting changes in the water quality of Lake Kasumigaura in Japan. The Canadian Journal of Statistics 48: 518–534; 2020 © 2020 Statistical Society of Canada

中文翻译：

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周期性时间序列的非参数变化点检测

我们考虑在已知周期内检测周期性和自相关数据分布中的多个变化。为了解决周期性问题，我们通过将向量观测值排列在矩阵中来变换其序列，从而生成一系列独立且均布的矩阵观测值。我们提出了检验矩阵分布相等性的方法，并提出了可以使用E-divivive算法应用于矩阵观测的方法。我们表明，周期性和自相关会降低现有的变更检测方法的性能，因为它们会使这些过程旨在发现的变更变得模糊。当周期效应压倒真实变化时，忽略周期的方法将无法检测周期时间序列的均值和方差的变化，所提出的方法可以大功率检测这种变化。我们通过检测日本霞浦湖水质的变化来说明所提出的方法。《加拿大统计杂志》 48：518–534；2020©2020加拿大统计学会