Identification of cointegrating relations in I(2) vector autoregressive models

This paper discusses identification within a new parametrization for I(2) systems, where the integral and proportional control cointegrating relations are not necessarily orthogonal. The new parametrization, while equivalent to previously proposed ones, gives more flexibility in choosing the variables to include in first differences in the integral and proportional control term. We discuss the joint identification of the cointegrating relations, providing rank and order conditions. We discuss likelihood estimation, and propose a simple alternating algorithm for likelihood-maximization, under the cases of under- exact- and over-identification. An illustration on US consumption is also