Title: Detecting change-points in time series via ordinal pattern probabilities
Authors: Alexander Schnurr - University Siegen (Germany) [presenting]
Herold Dehling - Ruhr-University Bochum (Germany)
Jeannette Woerner - TU Dortmund (Germany)
Ines Muenker - University of Siegen (Germany)
Jannis Buchsteiner - Ruhr-University Bochum (Germany)
Annika Betken - Ruhr-Universitat Bochum (Germany)
Abstract: Ordinal patterns describe the order structure of consecutive 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. We present limit theorems for ordinal pattern probabilities and tests for change-points in the short-range dependent as well as in the long-range dependent setting. In the long-range dependent case, we investigate the ordinal information of a subordinated Gaussian process with a non-summable autocovariance function. We establish the asymptotic behavior of different estimators for ordinal pattern probabilities by using a multivariate Hermite decomposition; the limits we obtain (normal -vs- Rosenblatt) depend on the Hermite rank of the functions we consider.