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Multiple Time Series Regression with Integrated Processes

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Author Info
Peter C.B. Phillips () (Cowles Foundation, Yale University)
Steven N. Durlauf (Cowles Foundation, Yale University)

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Abstract

This paper develops a general asymptotic theory of regression for processes which are integrated of order one. The theory includes vector autoregressions and multivariate regressions amongst integrated processes that are driven by innovation sequences which allow for a wide class of weak dependence and heterogeneity. The models studied cover cointegrated systems and quite general linear simultaneous equations systems with contemporaneous regressor-error correlation and serially correlated errors. Problems of statistical testing in vector autoregressions and multivariate regressions with integrated processes are also studied. It is shown that the asymptotic theory for conventional tests involves major departures from classical theory and raises new and important issues of the presence of nuisance parameters in the limiting distribution theory.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 768.

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Length: 43 pages
Date of creation: Sep 1985
Date of revision:
Publication status: Published in Review of Economic Studies (1986), 53: 473-495
Handle: RePEc:cwl:cwldpp:768

Note: CFP 659.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Integrated process; multivariate functional CLT; asymptotic theory for stationary VAR's;

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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. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June. [Downloadable!] (restricted)
  2. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-87, December. [Downloadable!] (restricted)
  3. Robert B. Litterman, 1984. "Forecasting with Bayesian vector autoregressions four years of experience," Staff Report 95, Federal Reserve Bank of Minneapolis. [Downloadable!]
  4. 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!]
    Other versions:
  5. Peter C.B. Phillips, 1985. "Asymptotic Expansions in Nonstationary Vector Autoregressions," Cowles Foundation Discussion Papers 765, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  6. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September. [Downloadable!] (restricted)
  7. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December. [Downloadable!] (restricted)
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  8. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September. [Downloadable!] (restricted)
  9. Marsh, Terry A. & Merton, Robert C., 1984. "Dividend variability and variance bounds tests for the rationality of stock market prices," Working papers 1584-84., Massachusetts Institute of Technology (MIT), Sloan School of Management. [Downloadable!]
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  10. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation, Yale University, revised Feb 1986. [Downloadable!]
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  11. Peter C.B. Phillips, 1986. "Weak Convergence to the Matrix Stochastic Integral BdB," Cowles Foundation Discussion Papers 796, Cowles Foundation, Yale University. [Downloadable!]
  12. Ian Domowitz, 1985. "New Directions in Non-linear Estimation with Dependent Observations," Canadian Journal of Economics, Canadian Economics Association, vol. 18(1), pages 1-27, February. [Downloadable!] (restricted)
  13. Brillinger, David R & Hatanaka, Michio, 1969. "An Harmonic Analysis of Nonstationary Multivariate Economic Processes," Econometrica, Econometric Society, vol. 37(1), pages 131-41, January. [Downloadable!] (restricted)
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