A method for change point detection is proposed. We consider a univariate sequence of independent random variables with piecewise constant expectation and variance, apart from which the distribution may vary periodically. We aim to detect change points in both expectation and variance. For that, we propose a statistical test for the null hypothesis of no change points and an algorithm for change point detection. Both are based on a bivariate moving sum approach that jointly evaluates the mean and the empirical variance. The joint consideration helps improve inference compared with separate univariate approaches. We infer on the strength and the type of changes with confidence. Nonparametric methodology supports the analysis of diverse data. Additionally, a multiscale approach addresses complex patterns in change points and effects. We demonstrate the performance through theoretical results and simulation studies. A companion R-package jcp (available on CRAN) is discussed.

中文翻译：

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双变量变化点检测：联合检测期望和方差的变化

提出了一种变化点检测方法。我们考虑具有分段常数期望和方差的独立随机变量的单变量序列，除此之外，分布可能会周期性变化。我们的目标是检测期望和方差的变化点。为此，我们提出了无变化点的零假设的统计检验和变化点检测的算法。两者都基于联合评估均值和经验方差的双变量移动和方法。与单独的单变量方法相比，联合考虑有助于改进推理。我们有信心地推断出变化的强度和类型。非参数方法支持对不同数据的分析。此外，多尺度方法解决了变化点和影响的复杂模式。我们通过理论结果和模拟研究证明了性能。一个同伴讨论了R -package jcp（在 CRAN 上可用）。