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 may exhibit rather arbitrary behavior for moderate values of the observed series but we place almost no restrictions on their dynamics for moderate values of the observed series.