IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v24y2003i5p591-612.html
   My bibliography  Save this article

Locally Optimal Tests Against Unit Roots in Seasonal Time Series Processes

Author

Listed:
  • A. M. ROBERT TAYLOR

Abstract

This paper builds on the existing literature on tests of the null hypothesis of deterministic seasonality in a univariate time‐series process. Under the assumption of independent Gaussian errors, we derive the class of locally weighted mean most powerful invariant tests against unit roots at the zero and/or seasonal frequencies in a seasonally observed process. Representations for the limiting distributions of the proposed test statistics under sequences of local alternatives are derived, and the relationship with tests for corresponding moving average unit roots is explored. We also propose nonparametric modifications of these test statistics designed to have limit distributions which are free of nuisance parameters under weaker conditions on the errors. Our tests are shown to contain existing stationarity tests as special cases and to extend these tests in a number of useful directions.

Suggested Citation

  • A. M. Robert Taylor, 2003. "Locally Optimal Tests Against Unit Roots in Seasonal Time Series Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 591-612, September.
    • Handle: RePEc:bla:jtsera:v:24:y:2003:i:5:p:591-612
    DOI: 10.1111/1467-9892.00324
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9892.00324
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9892.00324?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    2. 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.
    3. 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.
    4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    5. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    6. 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.
    7. O. D. Anderson, 1992. "Partial Autocorrelation Properties For Non‐Stationary Autoregressive Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(6), pages 485-500, November.
    8. Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 157-166, April.
    9. Smith, Richard J. & Taylor, A. M. Robert, 1998. "Additional critical values and asymptotic representations for seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 85(2), pages 269-288, August.
    10. Joseph Beaulieu, J. & Miron, Jeffrey A., 1993. "Seasonal unit roots in aggregate U.S. data," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 305-328.
    11. Ghysels, Eric & Lee, Hahn S. & Noh, Jaesum, 1994. "Testing for unit roots in seasonal time series : Some theoretical extensions and a Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 62(2), pages 415-442, June.
    12. Hansen, Bruce E., 1992. "Testing for parameter instability in linear models," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 517-533, August.
    13. Caner, Mehmet, 1998. "A Locally Optimal Seaosnal Unit-Root Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 349-356, July.
    14. A. M. Robert Taylor, 1998. "Testing for Unit Roots in Monthly Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(3), pages 349-368, May.
    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. El Montasser, Ghassen, 2014. "The seasonal KPSS Test: some extensions and further results," MPRA Paper 54920, University Library of Munich, Germany.
    2. El Montasser, Ghassen, 2012. "The seasonal KPSS Test: some extensions and further results," MPRA Paper 45110, University Library of Munich, Germany, revised 04 Mar 2014.
    3. Taylor, A. M. Robert, 2005. "Variance ratio tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 124(1), pages 33-54, January.
    4. Ai, Xiaohui & Li, Wenbo V. & Liu, Guoqing, 2012. "Karhunen–Loeve expansions for the detrended Brownian motion," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1235-1241.
    5. Ghassen El Montasser, 2015. "The Seasonal KPSS Test: Examining Possible Applications with Monthly Data and Additional Deterministic Terms," Econometrics, MDPI, vol. 3(2), pages 1-16, May.
    6. Fabio Busetti, 2006. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 419-438.
    7. Anton Skrobotov, 2013. "On GLS-detrending for deterministic seasonality testing," Working Papers 0073, Gaidar Institute for Economic Policy, revised 2014.
    8. Caceres-Hernandez, Jose & Martin-Rodriguez, Gloria, 2015. "Splines and seasonal unit roots in weekly agricultural prices," 2015 Conference, August 9-14, 2015, Milan, Italy 211380, International Association of Agricultural Economists.
    9. Matei Demetrescu & Uwe Hassler, 2007. "Effect of neglected deterministic seasonality on unit root tests," Statistical Papers, Springer, vol. 48(3), pages 385-402, September.

    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. Burridge, Peter & Taylor, A. M. Robert, 2001. "On regression-based tests for seasonal unit roots in the presence of periodic heteroscedasticity," Journal of Econometrics, Elsevier, vol. 104(1), pages 91-117, August.
    2. Fabio Busetti, 2006. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 419-438.
    3. Anton Skrobotov, 2013. "On GLS-detrending for deterministic seasonality testing," Working Papers 0073, Gaidar Institute for Economic Policy, revised 2014.
    4. Rodrigues, Paulo M. M. & Taylor, A. M. Robert, 2004. "Alternative estimators and unit root tests for seasonal autoregressive processes," Journal of Econometrics, Elsevier, vol. 120(1), pages 35-73, May.
    5. Gabriel Pons Rotger, 2004. "Seasonal Unit Root Testing Based on the Temporal Aggregation of Seasonal Cycles," Economics Working Papers 2004-1, Department of Economics and Business Economics, Aarhus University.
    6. Ghassen El Montasser, 2015. "The Seasonal KPSS Test: Examining Possible Applications with Monthly Data and Additional Deterministic Terms," Econometrics, MDPI, vol. 3(2), pages 1-16, May.
    7. Smith, Richard J. & Robert Taylor, A. M., 2001. "Recursive and rolling regression-based tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 105(2), pages 309-336, December.
    8. Rotger, Gabriel Pons, "undated". "Testing for Seasonal Unit Roots with Temporally Aggregated Time Series," Economics Working Papers 2003-16, Department of Economics and Business Economics, Aarhus University.
    9. El Montasser, Ghassen, 2012. "The seasonal KPSS Test: some extensions and further results," MPRA Paper 45110, University Library of Munich, Germany, revised 04 Mar 2014.
    10. Taylor, A. M. Robert, 2005. "Variance ratio tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 124(1), pages 33-54, January.
    11. El Montasser, Ghassen, 2014. "The seasonal KPSS Test: some extensions and further results," MPRA Paper 54920, University Library of Munich, Germany.
    12. Paulo Rodrigues & Philip Hans Franses, 2005. "A sequential approach to testing seasonal unit roots in high frequency data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(6), pages 555-569.
    13. Paulo Rodrigues & Denise Osborn, 1999. "Performance of seasonal unit root tests for monthly data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 985-1004.
    14. Burridge, Peter & Robert Taylor, A. M., 2004. "Bootstrapping the HEGY seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 123(1), pages 67-87, November.
    15. Shipra Banik & Param Silvapulle, 1999. "Testing for Seasonal Stability in Unemployment Series: International Evidence," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 26(2), pages 123-139, June.
    16. L. A. Gil-Alana & P. M. Robinson, 2001. "Testing of seasonal fractional integration in UK and Japanese consumption and income," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(2), pages 95-114.
    17. Stephen Leybourne & A. M. Robert Taylor, 2003. "Seasonal Unit Root Tests Based on Forward and Reverse Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 441-460, July.
    18. Gregoir, Stephane, 2006. "Efficient tests for the presence of a pair of complex conjugate unit roots in real time series," Journal of Econometrics, Elsevier, vol. 130(1), pages 45-100, January.
    19. Smith, Richard J. & Taylor, A.M. Robert & del Barrio Castro, Tomas, 2009. "Regression-Based Seasonal Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 25(2), pages 527-560, April.
    20. Haldrup, Niels & Montanes, Antonio & Sanso, Andreu, 2005. "Measurement errors and outliers in seasonal unit root testing," Journal of Econometrics, Elsevier, vol. 127(1), pages 103-128, July.

    More about this item

    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:bla:jtsera:v:24:y:2003:i:5:p:591-612. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.