Before revision:  Specifically, we consider  higher-order nonlinear autoregressions that may exhibit rather arbitrary behavior for moderate values of the observed series and that behave in a near unit root manner for large values of the observed series.
After revision:  Specifically, we consider higher-order nonlinear autoregressions that behave similarly to a unit root process for large values of the observed series and that behave in a near unit root manner for large values of the observed series.