This paper generalizes the univariate results of Chan and Tran (1989,
Econometric Theory 5, 354-362) and Phillips (1990, Econometric Theory
6, 44-62) to multivariate time series. We develop the limit theory for
the least-squares estimate of a VAR(1) for a random walk with indepen
dent and identically distributed errors and for I(1) processes with we
akly dependent errors whose distributions are in the domain of attract
ion of a stable law. The limit laws are represented by functionals of
a stable process. A semiparametric correction is used in order to asym
ptotically eliminate the ''bias'' term in the limit law. These results
are also an extension of the multivariate limit theory for square-int
egrable disturbances derived by Phillips and Durlauf (1986, Review of
Economic Studies 53, 473-495). Potential applications include tests fo
r multivariate unit roots and cointegration.