Asymptotic Expansions in Nonstationary Vector Autoregressions

Peter C.B. Phillips

68 citations0/0 files storedEconometric Theory

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Abstract

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].

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References

1980Macroeconomics and Reality 1987Time Series Regression with a Unit Root 1983Forecasting and Conditional Projection Using Realistic Prior Distributions 1984Forecasting and conditional projection using realistic prior distributions 1986Multiple Time Series Regression with Integrated Processes 1985Atheoretical macroeconometrics: A critique 1986Forecasting with Bayesian Vector Autoregressions: Five Years of Experience 1980Brownian Motion

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