A new approach to the problem of identifying a nonlinear time series model is considered. We argue that cumulative lagged conditional mean and variance functions are the appropriate "signatures" of a nonlinear time series for the purpose of model identification, being analogous to cumulative distribution functions or cumulative hazard functions in iid models. We introduce estimators of the cumulative lagged conditional mean and variance functions and study their asymptotic properties. A goodness-of-fit test for parametric time series models is also developed.
"Identification of Nonlinear Time Series from First Order Cumulative Characteristics." Ann. Statist. 22 (1) 495 - 514, March, 1994. https://doi.org/10.1214/aos/1176325381