ADDENDUM TO “ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES”
证明在Park和Phillips关于积分时间序列非线性变换的渐近定理中，若函数局部可积且满足正则条件，则无需排除极点附近的样本量依赖区域。
Typically in time series econometrics, for many statistics, a rescaled integrated process is replaced with Brownian motion to find the limit distribution. For averages of functions of a rescaled integrated process, Park and Phillips have shown that this remains true for functions with poles, as long as a sample-size-dependent region around the poles is excluded from consideration, the function is locally integrable, and some other regularity conditions hold. In this addendum, I show that under some regularity conditions on the function under consideration, there is no need for such a sample-size-dependent region around the pole in Park and Phillips' theorem, as long as the function under consideration is locally integrable.The author thanks four anonymous referees and Professor Phillips for their comments and suggestions and Benedikt Pötscher for suggestions and for pointing out an error in a previous version of this paper.