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+
