Information processing features can detect behavioral regimes of dynamical systems

TL;DR

This paper introduces an information processing framework using Shannon mutual information to analyze and predict behavioral regimes in dynamical systems, applied to cellular automata and financial time series, revealing regime shifts and key predictive features.

Contribution

It develops a novel information-theoretic approach to quantify local interactions in dynamical systems and demonstrates its effectiveness on cellular automata and financial data.

Findings

Few features suffice for full predictability in cellular automata

Information integration (synergy) is the most predictive feature

Financial crises show regime shifts detectable by the framework

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 and study this at the microscopic scale is missing. Here we propose an 'information processing' framework based on Shannon mutual information quantities between the initial and future 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 for ECA is that only a few features are needed for full predictability and that the 'information integration' (synergy) feature is always most predictive. Finally we apply the formalism to foreign exchange (FX) and interest-rate swap (IRS) time series data and find that the 2008 financial crisis marks a sudden and sustained regime shift (FX and EUR IRS) resembling tipping point behavior. The USD IRS market exhibits instead a slow and steady progression which appears consistent with the hypothesis that this market is (part of) the driving force behind the crisis. Our work suggests that the proposed framework is a promising way of predicting emergent complex systemic behaviors in terms of the local information processing of units.