A new proof of the representation theorem for I(2) processes

In this paper matrix polynomial inversion - by Laurent expansion about a second order pole - is linked to partitioned inversion of a block matrix mirroring the underlying rank assumptions. This paves the way to find closed-form solutions for the principal-part coefficient matrices of the Laurent expansion entering the representation of I(2) processes and shaping their cointegration spaces. On this basis a neat formulation and a new proof of the representation theorem of I(2) processes are provided.