Addendum to “ Asymptotics for nonlinear transformations of integrated time series ” ∗

Typically in time series econometrics, for many statistics, a rescaled integrated process is replaced with Brownian motion in order 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 and the function is locally integrable. In this addendum, I show that 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.