A geometric approach in non-parametric Changepoint detection in circular data

Abstract: In many temporally ordered data sets, it is observed that the parameters of the underlying distribution change abruptly at unknown times. The detection of such changepoints is important for many applications. While this problem has been studied substantially in the linear data setup, not much work has been done for angular data. In this article, we utilize the intrinsic geometry of a torus to propose new non-parametric tests. First, we propose new tests for the existence of changepoint(s) in the concentration, and second, a test to detect mean direction and/or concentration. The limiting distributions of the test statistics are derived, and their powers are obtained using extensive simulation. It is seen that the tests have better power than the corresponding existing tests. The proposed methods have been implemented on three real-life data sets, revealing interesting insights. In particular, our method, when used to detect simultaneous changes in mean direction and concentration for hourly wind direction measurements of the cyclonic storm "Amphan," identified changepoints that could be associated with important meteorological events.