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Spectral Regression for Cointegrated Time Series

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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.

Suggested Citation

  • Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:872
    Note: CFP 796.
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    Citations

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    Cited by:

    1. Dean Corbae & Sam Ouliaris & Peter C. B. Phillips, 2002. "Band Spectral Regression with Trending Data," Econometrica, Econometric Society, vol. 70(3), pages 1067-1109, May.
    2. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
    3. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots," NBER Chapters, in: NBER Macroeconomics Annual 1991, Volume 6, pages 141-220, National Bureau of Economic Research, Inc.
    4. Dietmar Bauer & Martin Wagner, 2002. "Asymptotic Properties of Pseudo Maximum Likelihood Estimates for Multiple Frequency I(1) Processes," Diskussionsschriften dp0205, Universitaet Bern, Departement Volkswirtschaft.
    5. Peter C. B. Phillips, 2005. "Econometric Analysis of Fisher's Equation," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 125-168, January.
    6. Kang Hao & Inder, Brett, 1996. "Diagnostic test for structural change in cointegrated regression models," Economics Letters, Elsevier, vol. 50(2), pages 179-187, February.
    7. Assenmacher-Wesche, Katrin & Gerlach, Stefan, 2008. "Money growth, output gaps and inflation at low and high frequency: Spectral estimates for Switzerland," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 411-435, February.
    8. Assenmacher-Wesche, Katrin & Gerlach, Stefan, 2008. "Interpreting euro area inflation at high and low frequencies," European Economic Review, Elsevier, vol. 52(6), pages 964-986, August.
    9. Kitamura, Yuichi & Phillips, Peter C. B., 1997. "Fully modified IV, GIVE and GMM estimation with possibly non-stationary regressors and instruments," Journal of Econometrics, Elsevier, vol. 80(1), pages 85-123, September.
    10. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "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?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    11. Erik Hjalmarsson, 2006. "Inference in Long-Horizon Regressions," International Finance Discussion Papers 853, Board of Governors of the Federal Reserve System (U.S.).
    12. Phillips, Peter C.B., 2014. "Optimal estimation of cointegrated systems with irrelevant instruments," Journal of Econometrics, Elsevier, vol. 178(P2), pages 210-224.
    13. Peter C.B. Phillips, 1992. "Hyper-Consistent Estimation of a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 1040, Cowles Foundation for Research in Economics, Yale University.
    14. Phillips, Peter C B, 1994. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Econometrica, Econometric Society, vol. 62(1), pages 73-93, January.
    15. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    16. 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.
    17. Matteo Farnè & Angela Montanari, 2022. "A Bootstrap Method to Test Granger-Causality in the Frequency Domain," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 935-966, March.
    18. Eiji Kurozumi, 2002. "Testing For Periodic Stationarity," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 243-270.
    19. Muhammad Ahad & Zaheer Anwer, 2021. "Asymmetric impact of oil price on trade balance in BRICS countries: Multiplier dynamic analysis," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 2177-2197, April.
    20. Elliott, Graham & Stock, James H., 1994. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 672-700, August.
    21. Corbae, Dean & Ouliaris, Sam & Phillips, Peter C B, 1994. "A Reexamination of the Consumption Function Using Frequency Domain Regressions," Empirical Economics, Springer, vol. 19(4), pages 595-609.
    22. 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 for Research in Economics, Yale University.
    23. 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 for Research in Economics, Yale University.
    24. 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.
    25. 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.

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