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Asymptotic Expansions in Nonstationary Vector Autoregressions

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Author Info
Phillips, P. C. B.

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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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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 3 (1987)
Issue (Month): 01 (February)
Pages: 45-68
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Handle: RePEc:cup:etheor:v:3:y:1987:i:01:p:45-68_00

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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.:
  1. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January. [Downloadable!] (restricted)
  2. Robert B. Litterman, 1984. "Forecasting with Bayesian vector autoregressions four years of experience," Staff Report 95, Federal Reserve Bank of Minneapolis. [Downloadable!]
  3. 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. [Downloadable!]
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  4. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January. [Downloadable!] (restricted)
  5. Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers 768, Cowles Foundation, Yale University. [Downloadable!]
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  6. 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 463-85, March. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
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  8. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Peter C.B. Phillips, 1987. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals via Martingale Approximations," Cowles Foundation Discussion Papers 846, Cowles Foundation, Yale University. [Downloadable!]
  2. Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers 768, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  3. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  4. Steve Lawford & Michalis P. Stamatogiannis, 2004. "The Finite-Sample Effects of VAR Dimensions on OLS Bias, OLS Variance, and Minimum MSE Estimators: Purely Nonstationary Case," Public Policy Discussion Papers 04-05, Economics and Finance Section, School of Social Sciences, Brunel University. [Downloadable!]
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  5. Zhijie Xiao & Peter C.B. Phillips, 1998. "Higher Order Approximations for Wald Statistics in Cointegrating Regressions," Cowles Foundation Discussion Papers 1192, Cowles Foundation, Yale University. [Downloadable!]
  6. Allan Timmermann & M. Hashem Pesaran, 2003. "Small Sample Properties of Forecasts from Autoregressive Models under Structural Breaks," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
    Other versions:
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