  We propose new concepts in order to analyze and model the dependence
structure between two time series. Our methods rely exclusively on the order
structure of the data points. Hence, the methods are stable under monotone
transformations of the time series and robust against small perturbations or
measurement errors. Ordinal pattern dependence can be characterized by four
parameters. We propose estimators for these parameters, and we calculate their
asymptotic distributions. Furthermore, we derive a test for structural breaks
within the dependence structure. All results are supplemented by simulation
studies and empirical examples.
  For three consecutive data points attaining different values, there are six
possibilities how their values can be ordered. These possibilities are called
ordinal patterns. Our first idea is simply to count the number of coincidences
of patterns in both time series, and to compare this with the expected number
in the case of independence. If we detect a lot of coincident patterns, this
means that the up-and-down behavior is similar. Hence, our concept can be seen
as a way to measure non-linear `correlation'. We show in the last section, how
to generalize the concept in order to capture various other kinds of
dependence.
