Asymptotic Expansions in Nonstationary Vector Autoregressions
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 .
Volume (Year): 3 (1987)
Issue (Month): 01 (February)
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- Peter C.B. Phillips, 1982.
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1202, National Bureau of Economic Research, Inc.
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"Multiple Time Series Regression with Integrated Processes,"
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Wiley Blackwell, vol. 53(4), pages 473-95, August.
- Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers 768, Cowles Foundation for Research in Economics, Yale University.
- Robert B. Litterman, 1984. "Forecasting with Bayesian vector autoregressions four years of experience," Staff Report 95, Federal Reserve Bank of Minneapolis.
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