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A REPRESENTATION THEORY FOR POLYNOMIAL COFRACTIONALITY IN VECTOR AUTOREGRESSIVE MODELS

Published online by Cambridge University Press:  04 November 2009

Massimo Franchi
Massimo Franchi*
Affiliation:
Università di Roma “La Sapienza”
*
*Address correspondence to Massimo Franchi, Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza,” P. le Aldo Moro 5, 00185 Rome, Italy; e-mail: massimo.franchi@uniroma1.it.
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Abstract

We extend the representation theory of the autoregressive model in the fractional lag operator of Johansen (2008, Econometric Theory 24, 651–676). A recursive algorithm for the characterization of cofractional relations and the corresponding adjustment coefficients is given, and it is shown under which condition the solution of the model is fractional of order d and displays cofractional relations of order d − b and polynomial cofractional relations of order d − 2b,…, d − cb ≥ 0 for integer c; the cofractional relations and the corresponding moving average representation are characterized in terms of the autoregressive coefficients by the same algorithm. For c = 1 and c = 2 we find the results of Johansen (2008).

Type
ARTICLES
Information
Econometric Theory , Volume 26 , Issue 4 , August 2010 , pp. 1201 - 1217
Copyright
Copyright © Cambridge University Press 2009

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