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Testing for a Unit Root by Generalized Least Squares Methods in the Time and Frequency Domains

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Abstract

New time and frequency domain tests for the presence of a unit root are developed. The tests are based on generalized least squares (GLS) methods in both the time and the frequency domains. For the time domain tests, moving average processes are assumed for the error terms on the autoregression. For the frequency domain tests, general assumptions are made which allow for stationary and weakly dependent error processes. The limiting distributions of feasible GLS tests are derived under MA(1) errors in the time domain. This theory is extended to higher order moving average processes under an invertibility condition. The limiting distributions of both full and band spectrum tests in the frequency domain are also derived. All of these limiting distributions are shown to be free of nuisance parameters. Some results on test consistency are also reported. Extensive Monte Carlo simulations are performed to study the size and power of the proposed tests in finite samples.

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File URL: http://cowles.econ.yale.edu/P/cd/d08b/d0899.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 CFP 899.

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Length: 78 pages
Date of creation: Mar 1989
Date of revision:
Publication status: Published in Journal of Econometrics (1993), 59: 263-286
Handle: RePEc:cwl:cwldpp:899

Note: CFP 850.
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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

Related research

Keywords: Unit root; spectral methods; generalized least squares; asymptotic theory; Monte Carlo;

References

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  1. Peter C.B. Phillips & Sam Ouliaris & Joon Y. Park, 1988. "Testing for a Unit Root in the Presence of a Maintained Trend," Cowles Foundation Discussion Papers 880, Cowles Foundation for Research in Economics, Yale University.
  2. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  3. Engle, Robert F & Gardner, Roy, 1976. "Some Finite Sample Properties of Spectral Estimators of a Linear Regression," Econometrica, Econometric Society, vol. 44(1), pages 149-65, January.
  4. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
  5. 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.
  6. Engle, Robert F, 1980. "Exact Maximum Likelihood Methods for Dynamic Regressions and Band Spectrum Regressions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(2), pages 391-407, June.
  7. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
  8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  9. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
  10. Espasa, Antoni & Sargan, J Denis, 1977. "The Spectral Estimation of Simultaneous Equation Systems with Lagged Endogenous Variables," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 583-605, October.
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