Micro–Macro Changepoint Inference for Periodic Data Sequences

Existing changepoint approaches consider changepoints to occur linearly in time; one changepoint happens after another and they are not linked. However, data processes may have regularly occurring changepoints, for example, a yearly increase in sales of ice-cream on the first hot weekend. Using linear changepoint approaches here will miss more global features such as a decrease in sales of ice-cream due to other product availability. Being able to tease these global changepoint features from the more local (periodic) ones is beneficial for inference. We propose a periodic changepoint model to model this behavior using a mixture of a periodic and linear time perspective. Built around a Reversible Jump Markov chain Monte Carlo sampler, the Bayesian framework is used to study the local (periodic) changepoint behavior. To identify the optimal global changepoint positions we integrate the local changepoint model into the pruned exact linear time (PELT) search algorithm. We demonstrate that the method detects both local and global changepoints with high accuracy on simulated and motivating applications that share periodic behavior. Due to the micro–macro nature of the analysis, visualization of the results can be challenging. We additionally provide a unique perspective for changepoint visualizations in these data sequences. Supplementary Materials for this article are available online.

现有变点（changepoint）方法均假设变点在时间维度上线性发生：变点依次出现且相互独立。然而，实际数据生成过程往往存在周期性出现的变点，例如每年首个炎热周末到来时，冰淇淋销售额会出现季节性上涨。若采用线性变点方法对此类数据进行分析，则会遗漏诸多全局特征——例如因竞品上市导致的冰淇淋销售额下滑。能够从局部（周期性）变点中甄别分离出全局变点特征，对统计推断具有重要价值。为此，本文提出一种周期性变点模型，通过融合周期性与线性时间视角的混合框架对该类行为进行建模。本文基于可逆跳跃马尔可夫链蒙特卡洛（Reversible Jump Markov chain Monte Carlo）采样器构建贝叶斯框架，用于分析局部（周期性）变点的行为特征。为确定最优全局变点位置，我们将局部变点模型集成至剪枝精确线性时间（pruned exact linear time, PELT）搜索算法中。实验结果表明，该方法在具有周期性特征的模拟数据与示例应用场景中，均可高精度地同时检测出局部与全局变点。由于本分析兼具微观与宏观双重属性，对结果进行可视化存在一定难度。为此，本文针对这类数据序列中的变点可视化问题提供了一种全新的分析视角。本文的补充材料可在线获取。