This paper studies the statistical properties of vector autoregressions (VAR’s) for quite general multiple time series which are integrated of order one. Functional central limit theorems are given for multivariate partial sums of weakly dependent innovations and these are applied to yield ﬁrst order asymptotics in nonstationary VAR’s. Characteristic and cumulant functionals for generalized random processes are introduced as a means of developing a reﬁnement of central limit theory on function spaces. The theory is used to ﬁnd asymptotic expansions of the regression coeﬀicients in nonstationary VAR’s under very general conditions. The results are speciﬁed to the scalar case and are related to other recent work by the author in  and .
Phillips, Peter C.B., "Asymptotic Expansions in Nonstationary Vector Autoregressions" (1985). Cowles Foundation Discussion Papers. 1006.