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Multivariate Autoregression Of Order One With Infinite Variance Innovations

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  • Zarepour, M.
  • Roknossadati, S.M.

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.

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  • Zarepour, M. & Roknossadati, S.M., 2008. "Multivariate Autoregression Of Order One With Infinite Variance Innovations," Econometric Theory, Cambridge University Press, vol. 24(3), pages 677-695, June.
    • Handle: RePEc:cup:etheor:v:24:y:2008:i:03:p:677-695_08
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    Cited by:

    1. Fatma Ozgu Serttas, 2018. "Infinite-Variance Error Structure in Finance and Economics," International Econometric Review (IER), Econometric Research Association, vol. 10(1), pages 14-23, April.
    2. Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute.

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