Information Processing Features Can Detect Behavioral Regimes of Dynamical Systems

Abstract

In dynamical systems, local interactions between dynamical units generate correlations which are stored and transmitted throughout the system, generating the macroscopic behavior. However a framework to quantify exactly how these correlations are stored, transmitted, and combined at the microscopic scale is missing. Here we propose to characterize the notion of “information processing” based on all possible Shannon mutual information quantities between a future state and all possible sets of initial states. We apply it to the 256 elementary cellular automata (ECA), which are the simplest possible dynamical systems exhibiting behaviors ranging from simple to complex. Our main finding is that only a few information features are needed for full predictability of the systemic behavior and that the “information synergy” feature is always most predictive. Finally we apply the idea to foreign exchange (FX) and interest-rate swap (IRS) time-series data. We find an effective “slowing down” leading indicator in all three markets for the 2008 financial crisis when applied to the information features, as opposed to using the data itself directly. Our work suggests that the proposed characterization of the local information processing of units may be a promising direction for predicting emergent systemic behaviors.