Detecting Change-Points in Time Series by Maximum Mean Discrepancy of Ordinal Pattern Distributions

Abstract

As a new method for detecting change-points in high-resolution time series, we apply Maximum Mean Discrepancy to the distributions of ordinal patterns in different parts of a time series. The main advantage of this approach is its computational simplicity and robustness with respect to (non-linear) monotonic transformations, which makes it particularly well-suited for the analysis of long biophysical time series where the exact calibration of measurement devices is unknown or varies with time. We establish consistency of the method and evaluate its performance in simulation studies. Furthermore, we demonstrate the application to the analysis of electroencephalography (EEG) and electrocardiography (ECG) recordings.