Further results on the asymptotics for nonlinear transformations of integrated time series

This paper establishes various results involving functions of integrated processes. Two theorems-which improve similar results by Park and Phillips-are proved for averages of functions of an integrated process that has not been rescaled by the square root of sample size. In addition, two results are given that characterize asymptotic behavior of averages of nonintegrable functions of rescaled integrated processes; the observations close to the pole take over asymptotic behavior in that case. Throughout, we make the assumption that the innovations of the integrated process are a linear process.