Abstract
Natural systems are often complex and dynamic (i.e. nonlinear), making them difficult to understand using linear statistical approaches. Linear approaches are fundamentally based on correlation. Thus, they are ill-posed for dynamical systems, where correlation can occur without causation, and causation may also occur in the absence of correlation. “Mirage correlation” (i.e., the sign and magnitude of the correlation change with time) is a hallmark of nonlinear systems that results from state dependency. State dependency means that the relationships among interacting variables change with different states of the system. In recent decades, nonlinear methods that acknowledge state dependence have been developed. These nonlinear statistical methods are rooted in state space reconstruction, i.e. lagged coordinate embedding of time series data. These methods do not assume any set of equations governing the system but recover the dynamics from time series data, thus called empirical dynamic modeling (EDM). EDM bears a variety of utilities to investigating dynamical systems. Here, we provide a step-by-step tutorial for EDM applications with rEDM, a free software package written in the R language. Using model examples, we aim to guide users through several basic applications of EDM, including (1) determining the complexity (dimensionality) of a system, (2) distinguishing nonlinear dynamical systems from linear stochastic systems, and quantifying the nonlinearity (i.e. state dependence), (3) determining causal variables, (4) forecasting, (5) tracking the strength and sign of interaction, and (6) exploring the scenario of external perturbation. These methods and applications can be used to provide a mechanistic understanding of dynamical systems.
Highlights
A famous old Chinese saying: ‘‘A halo around the moon indicates the rising of wind; the damp on a plinth is a sign of approaching rain’’ is believed to be written by Xun Su
They are illposed for dynamical systems, where correlation can occur without causation, and causation may occur in
Nonlinear methods that acknowledge state dependence have been developed. These nonlinear statistical methods are rooted in state space reconstruction, i.e. lagged coordinate embedding of time series data
Summary
A famous old Chinese saying: ‘‘A halo around the moon indicates the rising of wind; the damp on a plinth is a sign of approaching rain’’ is believed to be written by Xun Su (approximated to appear in 1069AD in the Sung Dynasty of China). Sugihara and May 1990; Anderson et al 2008; Glaser et al 2014; Ye et al 2015a) These nonlinear statistical methods are rooted in state space reconstruction (SSR), i.e. lagged coordinate embedding of time series data (Takens 1981). In practice, we may lack the phytoplankton and fish data needed to reconstruct the dynamics; or, in a more general situation, we may not even know all the critical variables for the system To overcome these difficulties, Takens (1981) offered a solution by demonstrating that a shadow version of the attractor (motion vectors or phase space) governing the original process can be reconstructed from time series observations on a single variable in the process (for example, the time series of zooplankton abundance) using lagged coordinate embedding. We conclude by pointing readers to useful references for more advanced applications of the EDM framework
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
