Closed-form expressions for the regular part coefficients in matrix polynomial inversion and related results

Abstract

In this paper closed-form expressions for the coefficient matrices of the regular part of the Laurent expansion for a matrix-polynomial inverse about a pole are obtained. This sets the stage for deriving the dynamic multipliers of a vector autoregressive model (VAR) in a straightforward way.

Keywords and phrases:

• Core-nilpotent representation
• canonical-form representation
• Laurent expansion
• VAR-model solution
• dynamic multipliers