COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 765 "Asymptotic Expansions in Nonstationary Vector Autoregressions" Peter C.B. Phillips August 1985 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]. |
