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, e.g. 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.