Addendum to "asymptotics for nonlinear transformations of integrated time series" (vol 20, pg 627, 2004)

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.