A small sample correction for tests of hypotheses on the cointegrating vectors

The main purpose of the analysis of the cointegrated VAR model is conducting inference on the cointegrating relations. Asymptotic inference is χ2, but the asymptotic results are not accurate enough for small samples. Therefore, we derive here a correction factor, depending on sample size and parameters, for the likelihood ratio test of some linear hypotheses on the cointegrating space in a vector autoregressive model. We have to assume that the adjustment coefficients are known. The main idea is to condition on the common trends when calculating the correction factor. Some simulation experiments illustrate the findings.