Nonlinear regressions with integrated time series

An asymptotic theory is developed for nonlinear regression with integrated processes. The models allow for nonlinear effects from unit root time serie s and therefore deal with the case of parametric nonlinear cointegration. T he theory covers integrable and asymptotically homogeneous functions. Suffi cient conditions for weak consistency are given and a limit distribution th eory is provided. The rates of convergence depend on the properties of the nonlinear regression function, and are shown to be as slow as n(1/4) for in tegrable functions, and to be generally polynomial in n(1/2) for homogeneou s functions. For regressions with integrable functions, the limiting distri bution theory is mixed normal with mixing variates that depend on the sojou rn time of the limiting Brownian motion of the integrated process.