Asymptotic Expansions in Nonstationary Vector Autoregressions
研究了一阶单整过程的向量自回归的统计性质，给出了弱相依创新的多元部分和泛函中心极限定理，并用于非平稳VAR回归系数的渐近展开。
This paper studies the statistical properties of vector autoregressions (VAR's) for quite general multiple time series which are integrated processes 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 specialized to the scalar case and are related to other recent work by the author [21].