Alexander Schnurr

Date: 01 December 2021

Time: 12.45 - 12.15 Hours

Room: RA1501 & MS-Teams

Speaker: Prof. Dr. Alexander Schnurr


Title: An overview on applications of ordinal patterns and ordinal pattern dependence

Abstract: Ordinal patterns describe the order structure of data points over a small time horizon. Using a moving window approach we reduce the complexity of a time series by analyzing the sequence of ordinal patterns instead of the original data. The concepts have been established first in the theory of dynamical systems and have later been adapted by statisticians.

Ordinal pattern dependence is a new way of measuring the degree of dependence between time series. Since it only relies on the ordinal structure of the data, it is robust against monotone transformations and measurement errors. This method has proved to be useful already in the context of hydrological, financial as well as medical data. Using this concept it is possible to analyze whether the dependence structure between two time series changes over time.

We present limit theorems for ordinal pattern probabilities and tests for structural breaks in the short-range dependent setting. Furthermore, we give an outlook towards long-range dependence, extremal events and multivariate extensions.