Reconstructing nonlinear structure in regression residuals

Phase space reconstruction is investigated as a diagnostic tool for uncovering structure of nonlinear processes in regression residuals. Results in the form of phase portraits (e.g. scatter plots of reconstructed dynamical systems) and descriptive statistics provide information that can identify underlying structural components from stochastic data outcomes, even in cases where such data appear essentially random, and provide insights categorizing structural components into functional classes to inform econometric/time series modeling efforts. Empirical evidence supporting this approach is provided using simulations from an Ikeda mapping. An application to US hops exports is used to illustrate the application of the approach.