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Testing for seasonal unit roots by frequency domain regression

Author

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

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. Moreover, our analysis allows for (possibly infinite order) moving average behaviour in the shocks, while extant large sample results pertaining to the Hylleberg et al. (1990) type tests are based on the assumption of a finite autoregression. 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

  • Marcus J. Chambers & Joanne S. Ercolani & A. M. Robert Taylor, 2010. "Testing for seasonal unit roots by frequency domain regression," Discussion Papers 10/02, University of Nottingham, Granger Centre for Time Series Econometrics.
    • Handle: RePEc:not:notgts:10/02
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    File URL: https://www.nottingham.ac.uk/research/groups/grangercentre/documents/10-02.pdf
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    References listed on IDEAS

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    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.
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    5. 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.
    6. 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.
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    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, June.
    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.
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    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.
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    Cited by:

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    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.

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    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

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