IDEAS home Printed from https://ideas.repec.org/p/bos/wpaper/wp2005-026.html
   My bibliography  Save this paper

Testing for Shifts in Trend with an Integrated or Stationary Noise Component

Author

Listed:
  • Pierre Perron

    (Department of Economics, Boston University)

  • Tomoyoshi Yabu

    (Department of Economics, Boston University)

Abstract

This paper considers the problem of testing for structural changes in the trend function of a univariate time series without any prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. We propose a new approach that builds on the work of Perron and Yabu (2005), based on a Feasible Quasi Generalized Least Squares procedure that uses a superefficient estimate of the sum of autoregressive parameters á when á = 1. In the case of a known break date, the resulting Wald test has a chi- square limit distribution in both the I(0) and I(1) cases. When the break date is unknown, the Exp function of Andrews and Ploberger (1994) yields a test with identical limit distributions in the two cases so that a testing procedure with nearly the same size in the I(0) and I(1) cases can be obtained. To improve the finite sample properties of the tests, we used the bias corrected version of the OLS estimate of á proposed by Roy and Fuller (2001). We show our procedure to be substantially more powerful then currently available alternatives and also to have a power function that is close to that attainable if we knew the true value of á in many cases. The extension to the case of multiple breaks is also discussed.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Pierre Perron & Tomoyoshi Yabu, 2005. "Testing for Shifts in Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2005-026, Boston University - Department of Economics.
    • Handle: RePEc:bos:wpaper:wp2005-026
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
    2. 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.
    3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    4. Robin L. Lumsdaine & David H. Papell, 1997. "Multiple Trend Breaks And The Unit-Root Hypothesis," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 212-218, May.
    5. Kormendi, Roger C & Meguire, Philip, 1990. "A Multicountry Characterization of the Nonstationarity of Aggregate Output," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 22(1), pages 77-93, February.
    6. Vogelsang, Timothy J & Perron, Pierre, 1998. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1073-1100, November.
    7. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Estimating deterministic trends with an integrated or stationary noise component," Journal of Econometrics, Elsevier, vol. 151(1), pages 56-69, July.
    8. Ben-David, Dan & Papell, David H., 1995. "The great wars, the great crash, and steady state growth: Some new evidence about an old stylized fact," Journal of Monetary Economics, Elsevier, vol. 36(3), pages 453-475, December.
    9. Anindya Roy & Barry Falk & Wayne A. Fuller, 2004. "Testing for Trend in the Presence of Autoregressive Error," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1082-1091, December.
    10. Tatsuma Wada & Pierre Perron, 2005. "Trend and Cycles: A New Approach and Explanations of Some Old Puzzles," Computing in Economics and Finance 2005 252, Society for Computational Economics.
    11. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    12. Vogelsang, Timothy J., 1997. "Wald-Type Tests for Detecting Breaks in the Trend Function of a Dynamic Time Series," Econometric Theory, Cambridge University Press, vol. 13(6), pages 818-848, December.
    13. Ben-David, D. & Papell, D.H., 1995. "The Great War, The Great Crash and Steady State Growth: Some New Evidence an Old Stylized Fact," Papers 36-95, Tel Aviv - the Sackler Institute of Economic Studies.
    14. repec:cup:etheor:v:13:y:1997:i:6:p:818-49 is not listed on IDEAS
    15. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    16. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    17. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
    18. Pierre Perron, 2005. "Dealing with Structural Breaks," Boston University - Department of Economics - Working Papers Series WP2005-017, Boston University - Department of Economics.
    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. Travaglini, Guido, 2007. "The U.S. Dynamic Taylor Rule With Multiple Breaks, 1984-2001," MPRA Paper 3419, University Library of Munich, Germany, revised 15 Jun 2007.
    2. Mohitosh Kejriwal & Claude Lopez, 2013. "Unit Roots, Level Shifts, and Trend Breaks in Per Capita Output: A Robust Evaluation," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 892-927, November.
    3. Skrobotov, Anton, 2020. "Survey on structural breaks and unit root tests," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 58, pages 96-141.
    4. Mohitosh Kejriwal & Pierre Perron, 2010. "A sequential procedure to determine the number of breaks in trend with an integrated or stationary noise component," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 305-328, September.
    5. Nuno Sobreira & Luis C. Nunes & Paulo M. M. Rodrigues, 2014. "Characterizing Economic Growth Paths Based On New Structural Change Tests," Economic Inquiry, Western Economic Association International, vol. 52(2), pages 845-861, April.
    6. Antonio E. Noriega & Daniel Ventosa‐Santaulària, 2006. "Spurious Regression Under Broken‐Trend Stationarity," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 671-684, September.
    7. Russo, Emanuele & Foster-McGregor, Neil & Verspagen, Bart, 2019. "Characterizing growth instability: new evidence on unit roots and structural breaks in long run time series," MERIT Working Papers 2019-026, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    8. Sobreira, Nuno & Nunesz, Luis C. & Rodriguesz, Paulo M. M., 2012. "Neoclassical, semi-endogenous or endogenous growth theory? Evidence based on new structural change tests," Insper Working Papers wpe_291, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    9. Emanuele Russo & Neil Foster-McGregor, 2022. "Characterizing growth instability: new evidence on unit roots and structural breaks in countries’ long run trajectories," Journal of Evolutionary Economics, Springer, vol. 32(2), pages 713-756, April.
    10. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    11. Kim, Dukpa & Perron, Pierre, 2009. "Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses," Journal of Econometrics, Elsevier, vol. 148(1), pages 1-13, January.
    12. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
    13. Paresh Kumar Narayan & Seema Narayan, 2010. "Are business cycles stationary fluctuations around a deterministic trend? Empirical evidence from 79 developing countries," International Review of Applied Economics, Taylor & Francis Journals, vol. 24(6), pages 649-664.
    14. Kurozumi, Eiji, 2002. "Testing for stationarity with a break," Journal of Econometrics, Elsevier, vol. 108(1), pages 63-99, May.
    15. Ghoshray, Atanu & Kejriwal, Mohitosh & Wohar, Mark E., 2011. "Breaking Trends and the Prebisch-Singer Hypothesis: A Further Investigation," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 120387, European Association of Agricultural Economists.
    16. Richard Bluhm & Denis de Crombrugghe & Adam Szirmai, 0. "Do Weak Institutions Prolong Crises? On the Identification, Characteristics, and Duration of Declines during Economic Slumps," The World Bank Economic Review, World Bank, vol. 34(3), pages 810-832.
    17. Firouz Fallahi & Gabriel Rodríguez, 2011. "Convergence In The Canadian Provinces: Evidence Using Unemployment Rates," Documentos de Trabajo / Working Papers 2011-322, Departamento de Economía - Pontificia Universidad Católica del Perú.
    18. Travaglini, Guido, 2008. "Dynamic GMM Estimation With Structural Breaks. An Application to Global Warming and its Causes," MPRA Paper 7108, University Library of Munich, Germany.
    19. Travaglini, Guido, 2010. "Dynamic Econometric Testing of Climate Change and of its Causes," MPRA Paper 23600, University Library of Munich, Germany.
    20. Alvaro Pereira & João Jalles & Martin Andresen, 2012. "Structural change and foreign direct investment: globalization and regional economic integration," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 11(1), pages 35-82, April.

    More about this item

    Keywords

    structural change; unit root; median unbaised estimates; GLS procedure; super efficient estimates;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:bos:wpaper:wp2005-026. 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: Program Coordinator (email available below). General contact details of provider: https://edirc.repec.org/data/decbuus.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.