MULTIVARIATE AUTOREGRESSION OF ORDER ONE WITH INFINITE VARIANCE INNOVATIONS

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+