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Multiple Regression with Integrated Time Series

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

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Abstract

Recent work on the theory of regression with integrated process is reviewed. This work is particularly relevant in economics where many financial series and macroeconomic time series exhibit nonstationary characteristics and are often well modeled individually as simple ARIMA processes. The theory makes extensive use of weak convergence methods and allows for integrated processes that are driven by quite general weakly dependent and possibly heterogeneously distributed innovations. The theory also includes near integrated time series, which have roots near unity, and cointegrated series, which move together over time but are individually nonstationary. A general framework for asymptotic analysis is given which involves limiting Gaussian functionals and extends the LAN and LAMN families of conventional asymptotic theory. An application to the Gaussian AR(1) is reported.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 852.

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Length: 41 pages
Date of creation: Nov 1987
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Publication status: Published in Contemporary Mathematics (1988), 80: 79-105
Handle: RePEc:cwl:cwldpp:852

Note: CFP 720.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
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: LAMN; LAN asymptotics; stochastic integral; unit roots; weak convergence; weak dependence;

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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. John Y. Campbell & N. Gregory Mankiw, 1987. "Permanent and Transitory Components in Macroeconomic Fluctuations," NBER Working Papers 2169, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  2. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-88, October. [Downloadable!] (restricted)
    Other versions:
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(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. Bunzel, Helle, 2003. "Fixed-b Asymptotics in Single Equation Cointegration Models with Endogenous Regressors," Staff General Research Papers 10685, Iowa State University, Department of Economics.
  2. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation, Yale University, revised Aug 1989. [Downloadable!]
    Other versions:
  3. Peter C.B. Phillips, 1999. "Descriptive Econometrics for Nonstationary Time Series with Empirical Illustrations," Cowles Foundation Discussion Papers 1219, Cowles Foundation, Yale University. [Downloadable!]
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  4. Peter C.B. Phillips, 1994. "Nonstationary Time Series and Cointegration: Recent Books and Themes for the Future," Cowles Foundation Discussion Papers 1081, Cowles Foundation, Yale University. [Downloadable!]
  5. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation, Yale University. [Downloadable!]
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  6. Peter C.B. Phillips, 1998. "Econometric Analysis of Fisher's Equation," Cowles Foundation Discussion Papers 1180, Cowles Foundation, Yale University. [Downloadable!]
  7. John C. Chao & Peter C.B. Phillips, 1997. "Model Selection in Partially Nonstationary Vector Autoregressive Processes with Reduced Rank Structure," Cowles Foundation Discussion Papers 1155, Cowles Foundation, Yale University. [Downloadable!]
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  8. Peter C.B. Phillips, 1995. "Impulse Response and Forecast Error Variance Asymptotics in Nonstationary VAR's," Cowles Foundation Discussion Papers 1102, Cowles Foundation, Yale University. [Downloadable!]
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  9. Hiro Y. Toda & Peter C.B. Phillips, 1991. "The Spurious Effect of Unit Roots on Exogeneity Tests in Vector Autoregressions: An Analytical Study," Cowles Foundation Discussion Papers 978, Cowles Foundation, Yale University. [Downloadable!]
  10. Josep Lluís Carrion-i-Silvestre & Andreu Sansó, 2005. "Testing the Null of Cointegration with Structural Breaks," DEA Working Papers 10, Universitat de les Illes Balears, Departament d'Economía Aplicada. [Downloadable!]
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  11. Helle Bunzel, 2004. "Fixed Bandwidth Asymptotics in Single Equation Models of Cointegration with an Application to Money Demand," Econometric Society 2004 North American Summer Meetings 219, Econometric Society. [Downloadable!]
  12. R.-P. Berben & D.J.C. van Dijk, 1998. "Does the absence of cointegration explain the typical findings in long horizon regressions?," Econometric Institute Report 145, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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  13. In Choi & Peter C.B. Phillips, 1997. "Regressions for Partially Identified, Cointegrated Simultaneous Equations," Cowles Foundation Discussion Papers 1162, Cowles Foundation, Yale University. [Downloadable!]
  14. T.J. Vogelsang & P.H. Franses, 2001. "Testing for common deterministic trend slopes," Econometric Institute Report 224, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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