  Distinguishing cause from effect is a scientific challenge resisting
solutions from mathematics, statistics, information theory and computer
science. Compression-Complexity Causality (CCC) is a recently proposed
interventional measure of causality, inspired by Wiener-Granger's idea. It
estimates causality based on change in dynamical compression-complexity (or
compressibility) of the effect variable, given the cause variable. CCC works
with minimal assumptions on given data and is robust to irregular-sampling,
missing-data and finite-length effects. However, it only works for
one-dimensional time series. We propose an ordinal pattern symbolization scheme
to encode multidimensional patterns into one-dimensional symbolic sequences,
and thus introduce the Permutation CCC (PCCC), which retains all advantages of
the original CCC and can be applied to data from multidimensional systems with
potentially hidden variables. PCCC is tested on numerical simulations and
applied to paleoclimate data characterized by irregular and uncertain sampling
and limited numbers of samples.
