Testing for the cointegrating rank of a VAR process with a time trend

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 time trends in the system. In practice, these characteristics are often unknown. Therefore, modified tests are considered which allow for deterministic linear trends in the data generation process (DGP). The tests are based on the Lagrange multiplier (LM) principle and, in contrast to likelihood ratio (LR) tests proposed for this situation, our tests take into account the cointegrating rank specified under the null hypothesis in estimating the trend parameters. The tests are shown to have nonstandard limiting distributions which do not depend on deterministic terms and have better local power and small sample properties than the competing LR tests in many situations.