  We analyze the ordinal structure of long-range dependent time series. To this
end, we use so called ordinal patterns which describe the relative position of
consecutive data points. We provide two estimators for the probabilities of
ordinal patterns and prove limit theorems in different settings, namely
stationarity and (less restrictive) stationary increments. In the second
setting, we encounter a Rosenblatt distribution in the limit. We prove more
general limit theorems for functions with Hermite rank 1 and 2. We derive the
limit distribution for an estimation of the Hurst parameter $H$ if it is higher
than 3/4. Thus, our theorems complement results for lower values of $H$ which
can be found in the literature. Finally, we provide some simulations that
illustrate our theoretical results.
