  The coupling complexity index is an information measure introduced within the
framework of ordinal symbolic dynamics. This index is used to characterize the
complexity of the relationship between dynamical system components. In this
work, we clarify the meaning of the coupling complexity by discussing in detail
some cases leading to extreme values, and present examples using synthetic data
to describe its properties. We also generalize the coupling complexity index to
the multivariate case and derive a number of important properties by exploiting
the structure of the symmetric group. The applicability of this index to the
multivariate case is demonstrated with a real-world data example. Finally, we
define the coupling complexity rate of random and deterministic time series.
Some formal results about the multivariate coupling complexity index have been
collected in an Appendix.
