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

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Abstract

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.
Original languageEnglish
Pages (from-to)147-155
Number of pages9
JournalFAR EAST JOURNAL OF THEORETICAL STATISTICS
Volume27
Publication statusPublished - 2009

Keywords

  • core-nilpotent decomposition
  • pole and integration orders
  • unified representation theorem

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