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Title: Ordinal pattern-based time series analysis Authors:  Annika Betken - University of Twente (Netherlands) [presenting]
Herold Dehling - Ruhr-University Bochum (Germany)
Alexander Schnurr - University Siegen (Germany)
Jannis Buchsteiner - Ruhr-University Bochum (Germany)
Jeannette Woerner - TU Dortmund (Germany)
Ines Nuessgen - University of Siegen (Germany)
Abstract: In time series analysis, ordinal patterns describe the relative position of consecutive data points generated by a stochastic process. Among other things, estimators are considered for the probabilities of occurrence of ordinal patterns (ordinal pattern probabilities) in time series. We investigate the statistical properties of these estimators in discrete-time Gaussian processes and establish limit theorems that describe the asymptotic distribution of the considered estimators. Additionally, we consider a measure of dependence between two-time series that is based on ordinal patterns (so-called ordinal pattern dependence). Ordinal pattern dependence can be considered as a non-parametric and non-linear counterpart to Pearson's correlation that allows for modeling leverage effects and dependence structures between financial time series.