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Article

Ordinal Pattern Dependence in the Context of Long-Range Dependence

Department of Mathematics, Siegen University, Walter-Flex-Straße 3, 57072 Siegen, Germany
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Author to whom correspondence should be addressed.
Academic Editor: Christian H. Weiss
Entropy 2021, 23(6), 670; https://doi.org/10.3390/e23060670
Received: 28 April 2021 / Revised: 18 May 2021 / Accepted: 19 May 2021 / Published: 26 May 2021
(This article belongs to the Special Issue Time Series Modelling)
Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal information is taken into account to derive robust results on the dependence between the two processes. This article deals with ordinal pattern dependence for a long-range dependent time series including mixed cases of short- and long-range dependence. We investigate the limit distributions for estimators of ordinal pattern dependence. In doing so, we point out the differences that arise for the underlying time series having different dependence structures. Depending on these assumptions, central and non-central limit theorems are proven. The limit distributions for the latter ones can be included in the class of multivariate Rosenblatt processes. Finally, a simulation study is provided to illustrate our theoretical findings. View Full-Text
Keywords: ordinal patterns; time series; long-range dependence; multivariate data analysis; limit theorems ordinal patterns; time series; long-range dependence; multivariate data analysis; limit theorems
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MDPI and ACS Style

Nüßgen, I.; Schnurr, A. Ordinal Pattern Dependence in the Context of Long-Range Dependence. Entropy 2021, 23, 670. https://doi.org/10.3390/e23060670

AMA Style

Nüßgen I, Schnurr A. Ordinal Pattern Dependence in the Context of Long-Range Dependence. Entropy. 2021; 23(6):670. https://doi.org/10.3390/e23060670

Chicago/Turabian Style

Nüßgen, Ines, and Alexander Schnurr. 2021. "Ordinal Pattern Dependence in the Context of Long-Range Dependence" Entropy 23, no. 6: 670. https://doi.org/10.3390/e23060670

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