IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v178y2014ip2p243-258.html
   My bibliography  Save this article

Testing for seasonal unit roots by frequency domain regression

Author

Listed:
  • Chambers, Marcus J.
  • Ercolani, Joanne S.
  • Taylor, A.M. Robert

Abstract

This paper develops univariate seasonal unit root tests based on spectral regression estimators. An advantage of the frequency domain approach is that it enables serial correlation to be treated non-parametrically. We demonstrate that our proposed statistics have pivotal limiting distributions under both the null and near seasonally integrated alternatives when we allow for weak dependence in the driving shocks. This is in contrast to the popular seasonal unit root tests of, among others, Hylleberg et al. (1990) which treat serial correlation parametrically via lag augmentation of the test regression. Our analysis allows for (possibly infinite order) moving average behaviour in the shocks. The size and power properties of our proposed frequency domain regression-based tests are explored and compared for the case of quarterly data with those of the tests of Hylleberg et al. (1990) in simulation experiments.

Suggested Citation

  • Chambers, Marcus J. & Ercolani, Joanne S. & Taylor, A.M. Robert, 2014. "Testing for seasonal unit roots by frequency domain regression," Journal of Econometrics, Elsevier, vol. 178(P2), pages 243-258.
    • Handle: RePEc:eee:econom:v:178:y:2014:i:p2:p:243-258
    DOI: 10.1016/j.jeconom.2013.08.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407613001899
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2013.08.025?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
    ---><---

    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. 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.
    2. Choi, In & Phillips, Peter C. B., 1993. "Testing for a unit root by frequency domain regression," Journal of Econometrics, Elsevier, vol. 59(3), pages 263-286, October.
    3. 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.
    4. Eugene Canjels & Mark W. Watson, 1997. "Estimating Deterministic Trends In The Presence Of Serially Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 184-200, May.
    5. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2010. "Robust methods for detecting multiple level breaks in autocorrelated time series," Journal of Econometrics, Elsevier, vol. 157(2), pages 342-358, August.
    6. Burridge, Peter & Taylor, A M Robert, 2001. "On the Properties of Regression-Based Tests for Seasonal Unit Roots in the Presence of Higher-Order Serial Correlation," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 374-379, July.
    7. 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.
    8. Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2007. "Efficient tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 141(2), pages 548-573, December.
    9. Castro, Tomás del Barrio & Osborn, Denise R. & Taylor, A.M. Robert, 2012. "On Augmented Hegy Tests For Seasonal Unit Roots," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1121-1143, October.
    10. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    11. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882, January.
    12. Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2004. "Asymptotic Distributions For Regression-Based Seasonal Unit Root Test Statistics In A Near-Integrated Model," Econometric Theory, Cambridge University Press, vol. 20(4), pages 645-670, August.
    13. 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.
    14. Pesaran, M. Hashem & Timmermann, Allan, 2004. "How costly is it to ignore breaks when forecasting the direction of a time series?," International Journal of Forecasting, Elsevier, vol. 20(3), pages 411-425.
    15. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-1363, September.
    16. Chambers, Marcus J. & Roderick McCrorie, J., 2007. "Frequency domain estimation of temporally aggregated Gaussian cointegrated systems," Journal of Econometrics, Elsevier, vol. 136(1), pages 1-29, January.
    17. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
    18. 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.
    19. 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.
    20. Taylor, A M Robert, 2002. "Regression-Based Unit Root Tests with Recursive Mean Adjustment for Seasonal and Nonseasonal Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 269-281, April.
    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. Eroğlu, Burak Alparslan, 2019. "Wavelet variance ratio cointegration test and wavestrapping," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 298-319.
    2. Burak Eroglu, 2017. "Wavelet Variance Ratio Test And Wavestrapping For The Determination Of The Cointegration Rank," Working Papers 1706, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.
    3. Atle Oglend & Frank Asche, 2016. "Cyclical non-stationarity in commodity prices," Empirical Economics, Springer, vol. 51(4), pages 1465-1479, December.
    4. Burak Eroglu & Kemal Caglar Gogebakan & Mirza Trokic, 2017. "Fractional Seasonal Variance Ratio Unit Root Tests," Working Papers 1707, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.
    5. Sheng-Hung Chen & Song-Zan Chiou-Wei & Zhen Zhu, 2022. "Stochastic seasonality in commodity prices: the case of US natural gas," Empirical Economics, Springer, vol. 62(5), pages 2263-2284, May.

    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. del Barrio Castro, Tomás & Rodrigues, Paulo M.M. & Robert Taylor, A.M., 2018. "Semi-Parametric Seasonal Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 34(2), pages 447-476, April.
    2. Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2007. "Efficient tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 141(2), pages 548-573, December.
    3. Castro, Tomás del Barrio & Osborn, Denise R. & Taylor, A.M. Robert, 2012. "On Augmented Hegy Tests For Seasonal Unit Roots," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1121-1143, October.
    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. del Barrio Castro, Tomás & Osborn, Denise R., 2023. "Periodic Integration and Seasonal Unit Roots," MPRA Paper 117935, University Library of Munich, Germany, revised 2023.
    6. Tomás Barrio Castro & Andrii Bodnar & Andreu Sansó, 2017. "Numerical distribution functions for seasonal unit root tests with OLS and GLS detrending," Computational Statistics, Springer, vol. 32(4), pages 1533-1568, December.
    7. Tom�s del Barrio Castro & Denise R. Osborn & A.M. Robert Taylor, 2016. "The Performance of Lag Selection and Detrending Methods for HEGY Seasonal Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 35(1), pages 122-168, January.
    8. Tomas del Barrio Castro, 2007. "Using the HEGY Procedure When Not All Roots Are Present," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(6), pages 910-922, November.
    9. Luis C. Nunes & Paulo M. M. Rodrigues, 2011. "On LM‐type tests for seasonal unit roots in the presence of a break in trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 108-134, March.
    10. Atle Oglend & Frank Asche, 2016. "Cyclical non-stationarity in commodity prices," Empirical Economics, Springer, vol. 51(4), pages 1465-1479, December.
    11. Jansson Michael & Nielsen Morten Ørregaard, 2011. "Nearly Efficient Likelihood Ratio Tests for Seasonal Unit Roots," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-21, February.
    12. 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.
    13. 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.
    14. Harvey, David I. & van Dijk, Dick, 2006. "Sample size, lag order and critical values of seasonal unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2734-2751, June.
    15. Giuseppe Cavaliere & Anton Skrobotov & A. M. Robert Taylor, 2019. "Wild bootstrap seasonal unit root tests for time series with periodic nonstationary volatility," Econometric Reviews, Taylor & Francis Journals, vol. 38(5), pages 509-532, May.
    16. 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.
    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. Pami Dua & Lokendra Kumawat, 2005. "Modelling and Forecasting Seasonality in Indian Macroeconomic Time Series," Working papers 136, Centre for Development Economics, Delhi School of Economics.
    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

    Keywords

    Seasonal unit root tests; Moving average; Frequency domain regression; Spectral density estimator; Brownian motion;
    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

    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:178:y:2014:i:p2:p:243-258. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.