  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 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.
