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 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  and .
|Date of creation:||Aug 1985|
|Publication status:||Published in Econometric Theory (1987), 3: 45-68|
|Contact details of provider:|| Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA|
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.yale.edu/
More information through EDIRC
|Order Information:|| Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-485, March.
- P. C. B. Phillips & S. N. Durlauf, 1986.
"Multiple Time Series Regression with Integrated Processes,"
Review of Economic Studies,
Oxford University Press, vol. 53(4), pages 473-495.
- 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.
- Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
- Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1986. "Forecasting and conditional projection using realistic prior distribution," Staff Report 93, Federal Reserve Bank of Minneapolis.
- Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
- White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
- Robert B. Litterman, 1984. "Forecasting with Bayesian vector autoregressions four years of experience," Staff Report 95, Federal Reserve Bank of Minneapolis.
- Magnus, J.R. & Neudecker, H., 1980. "The elimination matrix : Some lemmas and applications," Other publications TiSEM 0e3315d3-846c-4bc5-928e-f, Tilburg University, School of Economics and Management.
- Phillips, P.C.B., 1983. "Exact small sample theory in the simultaneous equations model," Handbook of Econometrics,in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 8, pages 449-516 Elsevier.
- Peter C.B. Phillips, 1982. "Exact Small Sample Theory in the Simultaneous Equations Model," Cowles Foundation Discussion Papers 621, Cowles Foundation for Research in Economics, Yale University.
- Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-779, May. Full references (including those not matched with items on IDEAS)