Ordinal Pattern Dependence in the Context of Long-Range Dependence.

Area of Science:

• Statistics
• Time Series Analysis
• Econometrics

Background:

• Ordinal pattern dependence measures multivariate dependence using time series co-movement.
• Ordinal time series analysis incorporates ordinal information for robust dependence results.

Purpose of the Study:

• Investigate ordinal pattern dependence for time series with short- and long-range dependence.
• Analyze the limit distributions of ordinal pattern dependence estimators under various dependence structures.

Main Methods:

• Derivation of limit distributions for estimators of ordinal pattern dependence.
• Application of central and non-central limit theorems based on time series dependence assumptions.
• Characterization of limit distributions within the class of multivariate Rosenblatt processes.

Main Results:

• Theoretical findings on limit distributions for ordinal pattern dependence estimators.
• Demonstration of how different time series dependence structures influence these distributions.
• Identification of specific limit distributions, including multivariate Rosenblatt processes.

Conclusions:

• The study provides a theoretical framework for understanding ordinal pattern dependence in complex time series.
• Theoretical findings are validated through a simulation study, enhancing practical applicability.
• The research contributes to robust dependence measurement in time series analysis.