Segmentation and classification of time series using ordinal pattern distributions

Abstract

The distribution of ordinal patterns in time series has been found to reflect important qualitative features of the underlying system dynamics. Abrupt changes in the dynamics typically result in clearly visible differences between the distributions before and after the break. Recurring dynamical regimes can be discovered by classifying the distributions in different parts of the time series. This paper discusses two algorithms which exploit the relation between ordinal pattern distributions and system dynamics for the segmentation and classification of time series. The first algorithm employs a kernel-based statistic, the Maximum Mean Discrepancy of ordinal pattern distributions, to detect and locate change points in the time series. The second algorithm uses clustering of the ordinal pattern distributions to classify time series segments with similar dynamics. The methodology is applied to various real-life time series from physiology and economics.