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Spectral Regression for Cointegrated Time Series

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

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Abstract

This paper studies the use of spectral regression techniques in the context of cointegrated systems of multiple time series. Several alternatives are considered including efficient and band spectral methods as well as system and single equation techniques. It is shown that single equation spectral regressions suffer asymptotic bias and nuisance parameter problems that render these regressions impotent for inferential purposes. By contrast systems methods are shown to be covered by LAMN asymptotic theory, bringing the advantages of asymptotic media unbiasedness, scale nuisance parameters and the convenience of asymptotic chi-squared tests. System spectral methods also have advantages over full system direct maximum likelihood in that they do not require complete specification of the error processes. Instead they offer a nonparametric treatment of regression errors which avoids certain methodological problems of dynamic specification and permits additional generality in the class of error processes.

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File URL: http://cowles.econ.yale.edu/P/cp/p07b/p0796.pdf
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File URL: http://cowles.econ.yale.edu/P/cd/d08b/d0872.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 872.

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Length: 33 pages
Date of creation: Apr 1988
Date of revision:
Publication status: Published in William A. Barnett, James Powell and George E. Tauchen, eds., Nonparametric And Semiparametric Methods in Econometrics and Statistics: Proceedings of the Fifth International Symposium in Economic Theory and Econometrics, Cambridge University Press, 1991, pp. 413-435
Handle: RePEc:cwl:cwldpp:872

Note: CFP 796.
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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

For technical questions regarding this item, or to correct its listing, contact: (Glena Ames).

Related research
Keywords: ARMA Model; co-integration; error correction; LAMN family; nonparametric; spectral regression;

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Cited by:
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  1. Peter C.B. Phillips, 1992. "Hyper-Consistent Estimation of a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 1040, Cowles Foundation, Yale University. [Downloadable!]
  2. Marcus J. Chambers, 2001. "Cointegration and Sampling Frequency," Economics Discussion Papers 531, University of Essex, Department of Economics. [Downloadable!]
  3. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots," NBER Technical Working Papers 0100, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  4. Peter C.B. Phillips, 1993. "Fully Modified Least Squares and Vector Autoregression," Cowles Foundation Discussion Papers 1047, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  5. Peter C.B. Phillips, 1992. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Cowles Foundation Discussion Papers 1039, Cowles Foundation, Yale University. [Downloadable!]
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  6. Assenmacher-Wesche, Katrin & Gerlach, Stefan, 2006. "Money Growth, Output Gaps and Inflation at Low and High Frequency: Spectral Estimates for Switzerland," CEPR Discussion Papers 5723, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  7. Dean Corbea & Sam Ouliaris & Peter C.B. Phillips, 1991. "A Reexamination of the Consumption Function Using Frequency Domain Regressors," Cowles Foundation Discussion Papers 997, Cowles Foundation, Yale University. [Downloadable!]
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  8. Dean Corbae & Sam Ouliaris & Peter C.B. Phillips, 1997. "Band Spectral Regression with Trending Data," Cowles Foundation Discussion Papers 1163, Cowles Foundation, Yale University. [Downloadable!]
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  9. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation, Yale University. [Downloadable!]
  10. Assenmacher-Wesche, Katrin & Gerlach, Stefan, 2006. "Interpreting Euro Area Inflation at High and Low Frequencies," CEPR Discussion Papers 5632, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  11. Erik Hjalmarsson, 2006. "New methods for inference in long-run predictive regressions," International Finance Discussion Papers 853, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  12. Peter C.B. Phillips, 1991. "The Long-Run Australian Consumption Function Reexamined: An Empirical Exercise in Bayesian Influence," Cowles Foundation Discussion Papers 1000, Cowles Foundation, Yale University. [Downloadable!]
  13. Dietmar Bauer & Martin Wagner, 2002. "Asymptotic Properties of Pseudo Maximum Likelihood Estimates for Multiple Frequency I(1) Processes," Diskussionsschriften dp0205, Universitaet Bern, Departement Volkswirtschaft. [Downloadable!]
  14. Graham Elliott & James H. Stock, 1992. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," NBER Technical Working Papers 0122, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  15. Peter C. B. Phillips, 2006. "Optimal Estimation of Cointegrated Systems with Irrelevant Instruments," Cowles Foundation Discussion Papers 1547, Cowles Foundation, Yale University. [Downloadable!]
  16. Yuichi Kitamura & Peter C.B. Phillips, 1994. "Fully Modified IV, GIVE and GMM Estimation with Possibly Non-Stationary Regressions and Instruments," Cowles Foundation Discussion Papers 1082, Cowles Foundation, Yale University. [Downloadable!]
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  17. Peter C.B. Phillips, 1998. "Econometric Analysis of Fisher's Equation," Cowles Foundation Discussion Papers 1180, Cowles Foundation, Yale University. [Downloadable!]
  18. Richard A. Ashley & Randall J. Verbrugge., 2006. "Mis-Specification in Phillips Curve Regressions: Quantifying Frequency Dependence in This Relationship While Allowing for Feedback," Working Papers e06-11, Virginia Polytechnic Institute and State University, Department of Economics. [Downloadable!]
  19. Chambers, M.J. & McCrorie, J.R., 2004. "Frequency domain gaussian estimation of temporally aggregated cointegrated systems," Discussion Paper 40, Tilburg University, Center for Economic Research. [Downloadable!]
  20. Richard A. Ashley. & Randall J. Verbrugge., 2006. "Mis-Specification and Frequency Dependence in a New Keynesian Phillips Curve," Working Papers e06-12, Virginia Polytechnic Institute and State University, Department of Economics. [Downloadable!]
  21. Peter C.B. Phillips & In Choi, 1989. "Testing for a Unit Root by Generalized Least Squares Methods in the Time and Frequency Domains," Cowles Foundation Discussion Papers CFP 899, Cowles Foundation, Yale University. [Downloadable!]
  22. Eiji Kurozumi, 2002. "Testing For Periodic Stationarity," Econometric Reviews, Taylor and Francis Journals, vol. 21(2), pages 243-270. [Downloadable!] (restricted)
  23. James H. Stock & Mark W. Watson, 1989. "A Simple MLE of Cointegrating Vectors in Higher Order Integrated Systems," NBER Technical Working Papers 0083, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  24. Mototsugu Shintani, 2000. "A Simple Cointegrating Rank Test Without Vector Autoregression," Working Papers 0044, Department of Economics, Vanderbilt University. [Downloadable!]
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  25. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
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