Graph-based Change Point Detection for Functional Data

Modeling functions that are sequentially observed as functional time series is becoming increasingly common. In such models, it is often crucial to ensure data homogeneity. We investigate the sensitivity of graph-based change point detection for changes in the distribution of functional data that demarcate homogeneous regions. Related test statistics and thresholds for detection are given. A key factor in the efficacy of such tests is the graph construction. Practical considerations for constructing a graph on arbitrary data are explored. Simulation experiments investigate tuning parameters for graph construction and evaluate the graph-based methods in comparison to existing functional methods. In addition to sensitivity of lower and higher order changes, robustness to the tuning parameter choices, and practical recommendations, are shown. Applications to multi-year pedestrian counts, high-frequency asset returns, and continuous electricity prices corroborate the simulation results.