Identification of Temporal Hotspots of Distributional Change in Stress and Passive mHealth Data

Identifying temporal changes in self-reported stress and passively sensed behavioral measures is important for examining longitudinal patterns in mental health research. Conventional change point detection methods typically return isolated change points, while approaches that model relationships between stress and passive sensing variables may require explicit functional assumptions. These features can complicate the identification of potentially asynchronous distributional changes across paired series. We propose a hotspot detection framework, where hotspots are candidate temporal regions in which changes in statistical features of self-reported stress and passive sensing measures may occur at the same or nearby times. We extend the moving-sum scheme to detect changes within and across series, and construct hotspots using thresholding and bootstrap confidence-interval rules. The method does not require a specific functional relationship between series and summarizes changes as intervals rather than isolated time points. Simulation studies show that the proposed procedures achieve competitive detection rates, with performance depending on window size and the number of changes. The two hotspot rules exhibit trade-offs between retaining true change locations and constructing localized intervals. We further illustrate the method using four participants from the ALACRITY Phase I study, where the procedures identify candidate regions of potential temporal concordance between changes in daily self-reported stress and smartphone-derived behavioral measures.