IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v117y2003i1p21-53.html
   My bibliography  Save this article

Testing against stochastic trend and seasonality in the presence of unattended breaks and unit roots

Author

Listed:
  • Busetti, Fabio
  • Taylor, A. M. Robert

Abstract

This paper considers the problem of testing against stochastic trend and seasonality in the presence of structural breaks and unit roots at frequencies other than those directly under test, which we term unattended breaks and unattended unit roots respectively. We show that under unattended breaks the true size of the Kwiatkowski et. al. (1992) [KPSS] test at frequency zero and the Canova and Hansen (1995) [CH] test at the seasonal frequencies fall well below the nominal level under the null with an associated, often very dramatic, loss of power under the alternative. We demonstrate that a simple modification of the statistics can recover the usual limiting distribution appropriate to the case where there are no breaks, provided unit roots do not exist at any of the unattended frequencies. Where unattended unit roots occur we show that the above statistics converge in probability to zero under the null. However, computing the KPSS and CH statistics after pre-filtering the data is simultaneously efficacious against both unattended breaks and unattended unit roots, in the sense that the statistics retain their usual pivotal limiting null distributions appropriate to the case where neither occurs. The case where breaks may potentially occur at all frequencies is also discussed. The practical relevance of the theoretical contribution of the paper is illustrated through a number of empirical examples.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Busetti, Fabio & Taylor, A. M. Robert, 2003. "Testing against stochastic trend and seasonality in the presence of unattended breaks and unit roots," Journal of Econometrics, Elsevier, vol. 117(1), pages 21-53, November.
  • Handle: RePEc:eee:econom:v:117:y:2003:i:1:p:21-53
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(03)00117-9
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    2. Harvey, Andrew, 2001. "Testing in Unobserved Components Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(1), pages 1-19, January.
    3. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, vol. 16(02), pages 176-199, April.
    4. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    5. 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.
    6. Smith, Jeremy & Otero, Jesus, 1997. "Structural breaks and seasonal integration," Economics Letters, Elsevier, vol. 56(1), pages 13-19, September.
    7. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-436, July.
    8. Taylor, A M Robert, 2003. "Robust Stationarity Tests in Seasonal Time Series Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 156-163, January.
    9. 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.
    10. Taylor, A.M.R., 1999. "Locally Optimal Tests Against Seasonal Unit Roots," Discussion Papers 99-12, Department of Economics, University of Birmingham.
    11. 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.
    12. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    13. Canova, Fabio & Hansen, Bruce E, 1995. "Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 237-252, July.
    14. Philip Hans Franses & Timothy J. Vogelsang, 1998. "On Seasonal Cycles, Unit Roots, And Mean Shifts," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 231-240, May.
    15. Busetti, Fabio & Taylor, A. M. Robert, 2003. "Testing against stochastic trend and seasonality in the presence of unattended breaks and unit roots," Journal of Econometrics, Elsevier, vol. 117(1), pages 21-53, November.
    16. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    17. Hansen, Bruce E., 1992. "Testing for parameter instability in linear models," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 517-533, August.
    18. Hylleberg, Svend, 1995. "Tests for seasonal unit roots general to specific or specific to general?," Journal of Econometrics, Elsevier, vol. 69(1), pages 5-25, September.
    19. Fabio Busetti & Andrew Harvey, 2003. "Further Comments On Stationarity Tests In Series With Structural Breaks At Unknown Points," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 137-140, March.
    20. Hannan, E J & Terrell, R D & Tuckwell, N E, 1970. "The Seasonal Adjustment of Economic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(1), pages 24-52, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tu, Yundong & Yi, Yanping, 2017. "Forecasting cointegrated nonstationary time series with time-varying variance," Journal of Econometrics, Elsevier, vol. 196(1), pages 83-98.
    2. Wang, Dabin & Tomek, William G., 2004. "Commodity Prices And Unit Root Tests," 2004 Annual meeting, August 1-4, Denver, CO 20141, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    3. Su, Chi-Wei & Tsangyao, Chang & Chang, Hsu-Ling, 2011. "Purchasing power parity for fifteen Latin American countries: Stationary test with a Fourier function," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 839-845, October.
    4. Fabio Busetti & Silvia Fabiani & Andrew Harvey, 2006. "Convergence of Prices and Rates of Inflation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 863-877, December.
    5. Busetti, Fabio & Taylor, A. M. Robert, 2003. "Testing against stochastic trend and seasonality in the presence of unattended breaks and unit roots," Journal of Econometrics, Elsevier, vol. 117(1), pages 21-53, November.
    6. repec:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-016-0687-x is not listed on IDEAS
    7. Mahdi Barakchian, S., 2015. "Transmission of US monetary policy into the Canadian economy: A structural cointegration analysis," Economic Modelling, Elsevier, vol. 46(C), pages 11-26.
    8. Fok, D. & Franses, Ph.H.B.F. & Paap, R., 2005. "Performance of Seasonal Adjustment Procedures: Simulation and Empirical Results," Econometric Institute Research Papers EI 2005-30, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Eroğlu, Burak Alparslan & Yiğit, Taner, 2016. "A nonparametric unit root test under nonstationary volatility," Economics Letters, Elsevier, vol. 140(C), pages 6-10.
    10. Webel, Karsten, 2016. "A data-driven selection of an appropriate seasonal adjustment approach," Discussion Papers 07/2016, Deutsche Bundesbank.
    11. Wang, Dabin & Tomek, William G., 2004. "Commodity Prices And Unit Root Tests," Working Papers 127145, Cornell University, Department of Applied Economics and Management.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:eee:econom:v:117:y:2003:i:1:p:21-53. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.