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Efficient tests of the seasonal unit root hypothesis

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  • Rodrigues, Paulo M.M.
  • Taylor, A.M. Robert

Abstract

In this paper we derive, under the assumption of Gaussian errors with known error covariance matrix, asymptotic local power bounds for seasonal unit root tests for both known and unknown deterministic scenarios and for an arbitrary seasonal aspect. We demonstrate that the optimal test of a unit root at a given spectral frequency behaves asymptotically independently of whether unit roots exist at other frequencies or not. We also develop modified versions of the optimal tests which attain the asymptotic Gaussian power bounds under much weaker conditions. We further propose near-efficient regression-based seasonal unit root tests using pseudo-GLS de-trending and show that these have limiting null distributions and asymptotic local power functions of a known form. Monte Carlo experiments indicate that the regression-based tests perform well in finite samples.
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  • 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.
  • Handle: RePEc:eee:econom:v:141:y:2007:i:2:p:548-573
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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. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    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. 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. 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. 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.
    7. Breitung, Jörg & Franses, Philip Hans, 1998. "On Phillips–Perron-Type Tests For Seasonal Unit Roots," Econometric Theory, Cambridge University Press, vol. 14(2), pages 200-221, April.
    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. 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.
    10. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882, June.
    11. 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.
    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. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    14. Jeganathan, P., 1991. "On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 7(3), pages 269-306, September.
    15. 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.
    16. Paulo M. M. Rodrigues, 2002. "On LM type tests for seasonal unit roots in quarterly data," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 176-195, June.
    17. 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.
    18. Rodrigues, Paulo M.M., 2001. "Near Seasonal Integration," Econometric Theory, Cambridge University Press, vol. 17(1), pages 70-86, February.
    19. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-287, August.
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    Cited by:

    1. Atle Oglend & Frank Asche, 2016. "Cyclical non-stationarity in commodity prices," Empirical Economics, Springer, vol. 51(4), pages 1465-1479, December.
    2. 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.
    3. 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.
    4. Eroğlu, Burak Alparslan & Göğebakan, Kemal Çağlar & Trokić, Mirza, 2018. "Powerful nonparametric seasonal unit root tests," Economics Letters, Elsevier, vol. 167(C), pages 75-80.
    5. Tomas del Barrio Castro & Mariam Camarero & Cecilio Tamarit, 2013. "The trade balance in euro countries: a natural case study of periodic integration with a changing mean," Working Papers 1321, Department of Applied Economics II, Universidad de Valencia.
    6. 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.
    7. 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.
    8. Ikerne Valle & Kepa Astorkiza & Ignacio Díaz-Emparanza, 2017. "Measuring species concentration, diversification and dependency in a macro-fishery," Empirical Economics, Springer, vol. 52(4), pages 1689-1713, June.
    9. Anton Skrobotov, 2013. "On GLS-detrending for deterministic seasonality testing," Working Papers 0073, Gaidar Institute for Economic Policy, revised 2014.
    10. 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.
    11. Tomas Barrio Castro & Mariam Camarero & Cecilio Tamarit, 2015. "An analysis of the trade balance for OECD countries using periodic integration and cointegration," Empirical Economics, Springer, vol. 49(2), pages 389-402, September.
    12. 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.
    13. del Barrio Castro, Tomás & Hecq, Alain, 2016. "Testing for deterministic seasonality in mixed-frequency VARs," Economics Letters, Elsevier, vol. 149(C), pages 20-24.
    14. Tomás Barrio & Mariam Camarero & Cecilio Tamarit, 2019. "Testing for Periodic Integration with a Changing Mean," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 45-75, June.
    15. 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.
    16. Luis Gil-Alana, 2010. "A seasonal fractional multivariate model. A testing procedure and impulse responses for the analysis of GDP and unemployment dynamics," Empirical Economics, Springer, vol. 38(2), pages 471-501, April.
    17. Tang, Ling & Yu, Lean & He, Kaijian, 2014. "A novel data-characteristic-driven modeling methodology for nuclear energy consumption forecasting," Applied Energy, Elsevier, vol. 128(C), pages 1-14.
    18. Maxwell L. King & Sivagowry Sriananthakumar, 2015. "Point Optimal Testing: A Survey of the Post 1987 Literature," Monash Econometrics and Business Statistics Working Papers 5/15, Monash University, Department of Econometrics and Business Statistics.
    19. Bauer, Dietmar, 2019. "Periodic and seasonal (co-)integration in the state space framework," Economics Letters, Elsevier, vol. 174(C), pages 165-168.

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    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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