Ordinal Pattern Dependence in the Context of Long-Range Dependence

• Main Authors: Ines Nüßgen, Alexander Schnurr
• Format: Article
• Language: English
• Published: MDPI AG 2021-05-01
• Series: Entropy
• Subjects: ordinal patterns; time series; long-range dependence; multivariate data analysis; limit theorems
• Online Access: https://www.mdpi.com/1099-4300/23/6/670

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.