IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/899.html
   My bibliography  Save this paper

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

Author

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.

Suggested Citation

  • 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.
  • Handle: RePEc:cwl:cwldpp:899
    Note: CFP 850.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d08/d0899.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
    2. 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.
    3. 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 1057-1072, June.
    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(3), pages 468-497, December.
    5. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    6. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
    7. 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.
    8. 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.
    9. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
    10. Engle, Robert F & Gardner, Roy, 1976. "Some Finite Sample Properties of Spectral Estimators of a Linear Regression," Econometrica, Econometric Society, vol. 44(1), pages 149-165, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Campos, Julia & Ericsson, Neil R. & Hendry, David F., 1996. "Cointegration tests in the presence of structural breaks," Journal of Econometrics, Elsevier, vol. 70(1), pages 187-220, January.
    4. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    5. H. Youn Kim & Junsoo Lee, 2001. "Quasi-fixed inputs and long-run equilibrium in production: a cointegration analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(1), pages 41-57.
    6. James Davidson, 2013. "Cointegration and error correction," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 7, pages 165-188, Edward Elgar Publishing.
    7. Peter C.B. Phillips, 1991. "Unit Roots," Cowles Foundation Discussion Papers 998, Cowles Foundation for Research in Economics, Yale University.
    8. Peter C.B. Phillips & Werner Ploberger, 1992. "Time Series Modeling with a Bayesian Frame of Reference: Concepts, Illustrations and Asymptotics," Cowles Foundation Discussion Papers 1038, Cowles Foundation for Research in Economics, Yale University.
    9. Ashok Parikh, 1994. "Tests of real interest parity in international currency markets," Journal of Economics, Springer, vol. 59(2), pages 167-191, June.
    10. van Amano, Robert A & Norden, Simon, 1998. "Exchange Rates and Oil Prices," Review of International Economics, Wiley Blackwell, vol. 6(4), pages 683-694, November.
    11. Ireland, Peter N., 1999. "Does the time-consistency problem explain the behavior of inflation in the United States?," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 279-291, October.
    12. Isabel Cortés-Jiménez & Manuel Artís, 2005. "The role of the tourism sector in economic development - Lessons from the Spanish experience," ERSA conference papers ersa05p488, European Regional Science Association.
    13. M. T. Alguacil & V. Orts, 2003. "Inward Foreign Direct Investment and Imports in Spain," International Economic Journal, Taylor & Francis Journals, vol. 17(3), pages 19-38.
    14. Jacint Balaguer & Manuel Cantavella-Jorda, 2004. "Structural change in exports and economic growth: cointegration and causality analysis for Spain (1961-2000)," Applied Economics, Taylor & Francis Journals, vol. 36(5), pages 473-477.
    15. Vicente Meneu & Hipòlit Torró, 2003. "Asymmetric covariance in spot‐futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(11), pages 1019-1046, November.
    16. Frédérique Bec & Mélika Ben Salem & Marine Carrasco, 2010. "Detecting Mean Reversion in Real Exchange Rates from a Multiple Regime star Model," Annals of Economics and Statistics, GENES, issue 99-100, pages 395-427.
    17. Randolph & Xiao Qin & Tan Gee Kwang, 2004. "Unit Root Tests with Markov-Switching," Econometric Society 2004 Australasian Meetings 145, Econometric Society.
    18. Canzoneri, Matthew B. & Cumby, Robert E. & Diba, Behzad, 1999. "Relative labor productivity and the real exchange rate in the long run: evidence for a panel of OECD countries," Journal of International Economics, Elsevier, vol. 47(2), pages 245-266, April.
    19. repec:ebl:ecbull:v:7:y:2006:i:4:p:1-7 is not listed on IDEAS
    20. Mitch Kunce, 2022. "The Tenuous Ecological Divorce and Unemployment Link with Suicide: A U.S. Panel Analysis 1968-2020," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 11(3), pages 1-2.
    21. Eleni Constantinou & Avo Kazandjian & Georgios P. Kouretas & Vera Tahmazian, 2008. "Common Stochastic Trends Among The Cyprus Stock Exchange And The Ase, Lse And Nyse," Bulletin of Economic Research, Wiley Blackwell, vol. 60(4), pages 327-349, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:899. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.