The power of residual-based tests for cointegration when residuals are fractionally integrated

This paper is concerned with testing the null hypothesis of no cointegration among I(1) variables when the cointegration residuals are I(d) with 0 < d <1. This possibility is entertained with increasing frequency in many applications, (see e.g. Cheung and Lai 1993 Baillie and Bollerslev 1994 Booth and Tse 1995 or Baillie 1996 for examples. We consider the power of various cointegration tests both for the stationary case d < 5 and for the nonstationary case d > 5.