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MULTIVARIATE AUTOREGRESSION OF ORDER ONE WITH INFINITE VARIANCE INNOVATIONS

Published online by Cambridge University Press:  22 January 2008

M. Zarepour  and
S.M. Roknossadati
M. Zarepour*
Affiliation:
University of Ottawa
S.M. Roknossadati
Affiliation:
University of Ottawa
*
Address correspondence to Mahmoud Zarepour, Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Street, P.O. Box 450 STN A, Ottawa, Ontario K1N 6N5, Canada; e-mail: [email protected].
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Abstract

We consider the limiting behavior of a vector autoregressive model of order one (VAR(1)) with independent and identically distributed (i.i.d.) innovations vector with dependent components in the domain of attraction of a multivariate stable law with possibly different indices of stability. It is shown that in some cases the ordinary least squares (OLS) estimates are inconsistent. This inconsistency basically originates from the fact that each coordinate of the partial sum processes of dependent i.i.d. vectors of innovations in the domain of attraction of stable laws needs a different normalizer to converge to a limiting process. It is also revealed that certain M-estimates, with some regularity conditions, as an appropriate alternative, not only resolve inconsistency of the OLS estimates but also give higher consistency rates in all cases.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 3 , June 2008 , pp. 677 - 695
Copyright
Copyright © Cambridge University Press 2008

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