TY  - THES
A3  - Schnurr, Alexander
AB  - Ordinal pattern analysis provides a possibility to study dependence structures in multivariate time series with few assumptions on the underlying stochastic model. Focussing on a univariate time series, we discuss the concept of ordinal pattern probabilities that deals with the occuranceoof one fixed ordinal pattern within this time series. Based on this method, the dependence within the time series is investigated. Turning to the multivariate case, ordinal pattern dependence allows us to compare data sets by studying the probability of coincident ordinal patterns at the same points in time. Applying these two approaches we are able to detect linear as well as non-linear dependence. We extend the theoretical framework for estimators in the context of these two concepts to multivariate long-range dependent Gaussian time series, allowing for pure long-range dependence as well as for mixed cases of short- and long-range dependent univariate components. We provide limit theorems for functionals with Hermite rank 1 and 2, as it turns out that the estimators in the context of ordinal pattern analysis are represented by these two classes. For functionals with Hermite rank 2, the asymptotic distribution is non-Gaussian and follows a Rosenblatt distribution. Further, we investigate the differences in the asymptotics considering multivariate stationary Gaussian time series and multivariate Gaussian time series with stationary increments, which is less restrictive. A generalization to more flexible models in the context of ordinal pattern dependence is also provided. The first part of this thesis closes with a simulation study that illustrates the theoretical results. The second part of this work puts ordinal pattern dependence in the perspective of multivariate dependence measures. We compare ordinal pattern dependence to classical dependence measures like Pearson’s p and Kendall’s r.
By precisely distinguishing between measures that arise in a time series context and models that study dependence between or within multivariate random vectors, we identify differences and provide relations between ordinal pattern dependence and the classical approaches. Finally, a simulation study and a real-world data analysis in the field of hydrology that emphasizes the practical value of ordinal pattern dependence complete this work.
AU  - Nüßgen, Ines
DA  - 2021
DO  - 10.25819/ubsi/9979
KW  - Musteranalyse
KW  - Ordinal patterns
KW  - Long-range dependence
KW  - Limit theorems
KW  - Multivariate dependence measures
KW  - Multivariate data analysis
LA  - eng
PY  - 2021
TI  - Ordinal pattern analysis: limit theorems for multivariate long-range dependent Gaussian time series and a comparison to multivariate dependence measures
TT  - Ordinale Muster Analyse: Grenzwertsätze für mehrdimensionale langzeitabhängige Gaußsche Zeitreihen sowie der Vergleich mit mehrdimensionalen Abhängigkeitsmaßen
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:467-19650
Y2  - 2024-11-22T12:08:53
ER  -