Harnessing the power of Topological Data Analysis to detect change points in time series

We introduce a novel geometry-oriented methodology, based on the emerging tools of topological data analysis, into the change point detection framework. The key rationale is that change points are likely to be associated with changes in geometry behind the data generating process. While the applications of topological data analysis to change point detection are potentially very broad, in this paper we primarily focus on integrating topological concepts with the existing nonparametric methods for change point detection. In particular, the proposed new geometry-oriented approach aims to enhance detection accuracy of distributional regime shift locations. Our simulation studies suggest that integration of topological data analysis with some existing algorithms for change point detection leads to consistently more accurate detection results. We illustrate our new methodology in application to the two closely related environmental time series datasets -ice phenology of the Lake Baikal and the North Atlantic Oscillation indices, in a research query for a possible association between their estimated regime shift locations.