A test of r versus r-1 Cointegrating Vectors

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A parametric test for r versus r−1 cointegrating vectors is developed. The test exploits the fact that in a system of n I(1) variates the rth principal component is I(0) under the null but I(1) under the alternative. The statistic is parametric, is constructed using simple regression methods applied to principal components, follows a standard χ2 distribution and does not require normalisation restrictions on the cointegrating vectors. A Monte Carlo investigation indicates that providing the lag length in the pre-whitening procedure is chosen by means of nested significance tests, the test has good size and power properties in small samples.
Original languageEnglish
Pages (from-to)151-191
Number of pages40
JournalJournal of Econometrics
Issue number1
Publication statusPublished - Jan 1999


  • cointegration test
  • noninvertible moving average
  • unit roots
  • ARMA estimation
  • Johansen test

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