ADDENDUM TO “ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES”

Robert de Jong

Econometric Theory, 2004, vol. 20, issue 3, 627-635

Abstract: 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.

Date: 2004
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