FURTHER RESULTS ON THE ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES
改进了Park和Phillips关于积分过程函数平均值的渐近结果，给出了未按样本量平方根重新缩放和重新缩放后不可积函数的渐近行为。
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.