# 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 (e.g. testing hypotheses to explain mechanisms or processes, or, for predicting 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

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