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

Abstract

Standard tests for the cointegrating rank of a vector autoregressive (VAR) process have nonstandard limiting distributions which depend on the characteristics of intercept terms and other deterministic terms such as time trends in the data generation process. In practice these characteristics are often unknown. Therefore, modified tests are proposed with limiting distributions which do not depend on the characteristics of deterministic terms under the null hypothesis. The tests make use of lag augmentation, that is, a VAR 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 χ 2 limiting distributions are obtained in this way.