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Multiple Regression with Integrated Time Series

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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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File URL: http://cowles.econ.yale.edu/P/cd/d08b/d0852.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 852.

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

Note: CFP 720.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: LAMN; LAN asymptotics; stochastic integral; unit roots; weak convergence; weak dependence;

References

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  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.
  2. Campbell, John & Shiller, Robert, 1987. "Cointegration and Tests of Present Value Models," Scholarly Articles 3122490, Harvard University Department of Economics.
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Cited by:
  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 for Research in Economics, Yale University, revised Aug 1989.
  3. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  4. 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 for Research in Economics, Yale University.
  5. Peter C. B. Phillips, 2001. "Descriptive econometrics for non-stationary time series with empirical illustrations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 389-413.
  6. Peter C.B. Phillips, 1998. "Econometric Analysis of Fisher's Equation," Cowles Foundation Discussion Papers 1180, Cowles Foundation for Research in Economics, Yale University.
  7. Josep Lluís Carrion-i-Silvestre & Andreu Sansó, 2006. "Testing the Null of Cointegration with Structural Breaks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(5), pages 623-646, October.
  8. Peter C.B. Phillips, 1995. "Impulse Response and Forecast Error Variance Asymptotics in Nonstationary VAR's," Cowles Foundation Discussion Papers 1102, Cowles Foundation for Research in Economics, Yale University.
  9. In Choi & Peter C.B. Phillips, 1997. "Regressions for Partially Identified, Cointegrated Simultaneous Equations," Cowles Foundation Discussion Papers 1162, Cowles Foundation for Research in Economics, Yale University.
  10. 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.
  11. Peter C.B. Phillips, 1994. "Nonstationary Time Series and Cointegration: Recent Books and Themes for the Future," Cowles Foundation Discussion Papers 1081, Cowles Foundation for Research in Economics, Yale University.
  12. 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 for Research in Economics, Yale University.

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