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.
|Numero di pagine||9|
|Rivista||FAR EAST JOURNAL OF THEORETICAL STATISTICS|
|Stato di pubblicazione||Pubblicato - 2009|
- core-nilpotent decomposition
- pole and integration orders
- unified representation theorem