Causal Inference Using Multi-Channel Regime Switching Information Transfer Estimation

Carl-Henrik Dahlqvist^1,2

The past decade has seen the development of new methods to infer causal relationships in biological and socio-economic complex systems, following the expansion of network theory. Nevertheless, the standard estimation of causality still involves a single pair of time dependent variables which could be conditioned, in some instance, on its close environment. However, interactions may appear at a higher level between parts of the considered systems represented by more than one variable. We propose to study these types of relationships and develop a multi-channel framework, in the vein of Barrett and Barnett (Phys. Rev. E, 81 (2010)), allowing the inference of causal relationships between two sets of variables. Each channel represents the possible interaction between a variable of each sub-system. Based on this new framework, we develop two different multi-channel causality measures derived from the usual Granger causality to account for linear interactions and from the concept of transfer entropy for nonlinear contribution. Our measures provide different information about the inferred causal links: the strength of the global interaction between the two sub-systems, the average frequency of the channel switches and the channel contributing the most to the information transfer process for each time step. After having demonstrated the ability of our measures to infer linear as well as nonlinear interactions, we propose an application looking at the U.S. financial sector in order to better understand the interactions between individual financial institutions, as well as parts of the financial system. At the individual level, the considered channels between financial institutions are expressed both in terms of spectral representation using wavelet transform and probability distribution using quantile regressions. Beyond the application presented in the paper, this new multi-channel framework should be easy to implement in other fields of complex system science such as neuroscience, biology or physics.