Subpattern matching persistent homology for coupling complexity analysis of multivariate time series

We propose a new persistent homology approach to study the coupling complexity of multivariate time series. It subsumes the existing one based on ordinal patterns. In the proposed approach, we can choose the patterns used to construct filtered simplicial complexes that reflect the relations among the components of a given multivariate time series. We apply the proposed persistent homology based on binary patterns to binary multivariate time series generated by random Boolean networks. We argue that the total persistence of the filtered simplicial complexes serves as a coupling complexity measure and show that its average takes the maximum value near criticality of dynamical stability.