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The Power of Residual-Based Tests for Cointegration when Residuals Are Fractionally Integrated

By Walter Krämer and Francesc Marmol


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 ! 0:5) and for the nonstationary case (d 0:5). When the potential cointegrating relationship is known, this problem boils down to testing for unit roots against fractional alternatives, as discussed by e.g. Sowell (1990), Diebold and Rudebusch (1991), Hassler and Wolters (1994), Dolado and Marmol (1997) or Kr amer(1998). When the potential cointegrating relationship has to be estimated, we encounter the twin problems of nonstandard regression properties due to I(d)--disturbances and unobservability of the true residuals. While the second problem has been solved for the case where

Year: 1998
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