Empirical Dynamic Modeling (EDM)

Empirical dynamic modeling (EDM) is an emerging non-parametric framework for modeling nonlinear dynamic systems. EDM is based on the mathematical theory of reconstructing attractor manifolds from time series data (Takens 1981). EDM algorithms include simplex projection (Sugihara and May 1990), S-map (Sugihara 1994), multivariate embedding (Dixon, Milicich, and Sugihara 1999), convergent cross mapping (Sugihara et al. 2012), and multiview embedding (Ye and Sugihara 2016). These documents introduce the underlying theory, and illustrate analytical functionality with examples.

The core EDM algorithms are implemented in the cppEDM library. Python and R interfaces to the library are provided in the pyEDM and rEDM packages.

Motivation

Many analytic approaches use models as approximations of real world systems to test hypotheses, explain mechanisms, or, predict future outcomes. However, real world systems are often nonlinear and multidimensional, rendering explicit parametric equations problematic. Empirical models, which infer patterns and associations from the data instead of using discrete, hypothesized equations, represent a natural and flexible approach to modeling complex dynamics.

Foundations of EDM

Time Series as Observations of a Dynamic System

Prediction and system interactions

Given a state space reconstructed via lagged embedding, or, from multivariate observations, system prediction can be performed using simplex or S-map (Sequentially Locally Weighted Global Linear Maps) projection. S-map can also be used to assess variable interactions and infer the degree of system nonlinearity. To infer causal relationships between variables, Convergent Cross Mapping (CCM) can be applied. See the algorithms in depth section for details on these functions.