  We establish a definition of ordinal patterns for multivariate time series
data based on the concept of Tukey's halfspace depth. Given the definition of
these \emph{depth patterns}, we are interested in the probabilities of
observing specific patterns in a time series. For this, we consider the
relative frequency of depth patterns as natural estimators for their occurrence
probabilities. Depending on the choice of reference distribution and the
relation between reference and data distribution, we distinguish different
settings that are considered separately. Within these settings we study
statistical properties of ordinal pattern probabilities, establishing
consistency and asymptotic normality under the assumption of weakly dependent
time series data. Since our concept only depends on ordinal depth information,
the resulting values are robust under small perturbations and measurement
errors.
