Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models1

In this paper a bootstrap algorithm for a reduced rank vector autoregressive model with a restricted linear trend and independent, identically distributed errors is analyzed. For testing the cointegration rank, the asymptotic distribution under the hypothesis is the same as for the usual likelihood ratio test, so that the bootstrap is consistent. It is furthermore shown that a bootstrap procedure for determining the rank is asymptotically consistent in the sense that the probability of choosing the rank smaller than the true one converges to zero.