Elastic Functional Changepoint Detection

Detecting changepoints in functional data has become an important problem as interest in monitory of climatologies and other various processing monitoring situations has increased, where the data is functional in nature. The observed data often contains variability in amplitude ($y$-axis) and phase ($x$-axis). If not accounted for properly, incorrect changepoints can be detected, as well as underlying mean functions at those changes will be incorrect. In this paper, an elastic functional changepoint method is developed which properly accounts for these types of variability. Additionally, the method can detect amplitude and phase changepoints which current methods in the literature do not, as they focus solely on the amplitude changepoint. This method can easily be implemented using the functions directly, or to ease the computational burden can be computed using functional principal component analysis. We apply the method to both simulated data and real data sets to show its efficiency in handling data with phase variation with both amplitude and phase changepoints.