Statistical Inference in Possibly Integrated/Cointegrated Vector Autoregressions: Application to Testing for Structural Changes

We develop a new approach of statistical inference in possibly integrated/cointegrated vector autoregressions. Our method is built on the two previous approaches: the lag augmented approach by Toda and Yamamoto (1995) and the artificial autoregressions by Yamamoto (1996). We show that our estimator is asymptotically normally distributed irrespective of whether the variables are stationary or nonstationary, and that the Wald test statistic for the parameter restrictions has an asymptotic chi-square distribution. Using this method, we also propose to test for multiple structural changes. We show that our test statistics have the same limiting distributions as in the standard case, irrespective of whether the variables are stationary, purely integrated, or cointegrated.