Inference of vector autoregressive models with cointegration and scalar components

For the partially nonstationary vector autoregressive model of Ahn and Reinsel, I further assume that the first differenced series has scalar components of lower order and study estimation of these models along with asymptotic properties of the estimators. It is shown that Gaussian reduced rank estimation can be easily carried out by simple modification of the Ahn and Reinsel's method. The asymptotic distribution for the estimator of the nonstationary parameter is a locally asymptotically mixed normal, and for that of the stationary parameter is asymptotically a normal. Testing hypothesis of the assumed structure of scalar components, including serial correlation common feature, is briefly discussed. A numerical example is provided to illustrate the methods.