New insights into vector-autoregressive econometric models for core-nilpotent decomposition of the total effect matrix

This paper pinpoints the role played by the core-nilpotent decomposition of the total effect matrix in detecting the integration order of a vector autoregressive (VAR) econometric model and in establishing closed-form expressions for the coefficients of its solution. More specifically, after showing how the nilpotent-term index actually determines the pole order of the matrix-polynomial inverse operator underlying the VAR solution, this paper establishes a unified representation theorem for the generated process on a strictly algebraic basis.