Elastic Functional Changepoint Detection of Climate Impacts from Localized Sources 

Abstract: Functional data analysis (FDA) is an important research area, due to its broad applications across many disciplines where functional data is prevalent. An essential component in solving these problems is the registration of points across functional objects. Without proper registration the results are often inferior and difficult to interpret. The current practice in the FDA literature is to treat registration as a pre-processing step, using off-the-shelf alignment procedures, and follow it up with statistical analysis of the resulting data. In contrast, an elastic framework is a more comprehensive approach, where one solves for the registration and statistical inferences in a simultaneous fashion. Our goal is to use a metric with appropriate invariance properties, to form objective functions for alignment and to develop statistical models involving functional data. While these elastic metrics are complicated in general, we have developed a family of square-root transformations that map these metrics into simpler Euclidean metrics, thus enabling more standard statistical procedures. In this talk, we present a changepoint method for functional data which properly accounts for these types of invariances and demonstrate on simulated data and climate data from the eruption of Mt. Pinatubo in the Philippines in June 1991.