Empirical dynamic modeling (EDM) is an approach for understanding the inherent dynamics (i.e. rules, processes, mechanisms) that underlie time series observations.
For example, in the graphic above, the time series is formed from the observation of variable $z$ of the Lorenz Attractor. More generally, time series can be more complex projections from the underlying dynamic system. EDM describes a way to recover information about the system from the time series.
The approach relies on the theory of attractor reconstruction (also referred to as “state-space reconstruction” or “time-delay embedding”) to transform time series into approximations of the original dynamic system that the time series are observations of. This has applications for forecasting, causal inference, and more.
For the R package for empirical dynamic modeling, check out rEDM.
For a short video introduction, check out the following youtube playlist (~6 minutes total):