Topological Methods for Time Series Testing using Sublevel Set Persistence

Music City Center 

Sublevel set persistence diagrams from topological data analysis have found greater statistics and data science applications in recent years; e.g. in fields such as biomedical signal processing. In this talk, we detail two fundamental convergence results for such persistent diagrams for stationary time series and delineate their applications and efficacy in hypothesis testing for time series. Namely, we demonstrate both our strong law of large numbers and our central limit theorem for these topological statistics. We then discuss how these results apply to a wide variety of time series models and various functionals of the derived persistence diagrams. We will then discuss how these results can be applied to test for various characteristics of time series such as the presence of serial correlation and changepoints.