A lag augmentation test for the cointegrating rank of a VAR process

Standard tests for the cointegrating rank of a vector autoregressive (VAR) process have nonstandard limiting distributions which depend on the charact eristics of intercept terms and other deterministic terms such as time tren ds in the data generation process. In practice these characteristics are of ten unknown. Therefore, modified tests are proposed with limiting distribut ions which do not depend on the characteristics of deterministic terms unde r the null hypothesis. The tests make use of lag augmentation, that is, a V AR process of order p + 1 is fitted when the true order is p and the tests are based on the estimated coefficient matrices associated with the first p lags only. It is shown that chi(2) limiting distributions are obtained in this way. (C) 1999 Elsevier Science S.A. All rights reserved.