Reconstructing System Dynamics and Causal Interactions from Complex Time Series Data

Abstract. Data provide an essential portal to understanding real-world dynamic systems to which we have only limited access. Nonlinear Time Series Analysis (NLTS)—developed in the mathematical physics literature—is a new approach to empirical-dynamic analysis in the applied sciences, engineering, and social sciences. NLTS diagnostics test whether real-world dynamics are nonlinear and deterministic, and provide for directed exploration of deterministic structures capable of reproducing observed complexity. NLTS can be used to detect causal interactions among observed variables generated by real-world nonlinear dynamic systems, and extract a system of Ordinary Differential Equations that reproduces simulated dynamics corresponding to the dynamics reconstructed from observed data.