Far East Journal of Theoretical Statistics
Volume 27, Issue 2, Pages 147 - 155
(March 2009)
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NEW INSIGHTS INTO VECTOR-AUTOREGRESSIVE ECONOMETRIC MODELS FROM A CORE-NILPOTENT DECOMPOSITION OF THE TOTAL EFFECT MATRIX
Maria Grazia Zoia (Italy)
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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. |
Keywords and phrases: core-nilpotent decomposition, pole and integration orders, unified representation theorem. |
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