CFDP 765

Asymptotic Expansions in Nonstationary Vector Autoregressions


Publication Date: August 1985

Pages: 34


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 [17] and [19].


Asymptotic expansions, Vector autoregressions, Characteristic functionals, Generalized random processes

JEL Classification Codes:  211

See CFP: 679