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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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 141 (2007)
Issue (Month): 2 (December)
Pages: 548-573

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Handle: RePEc:eee:econom:v:141:y:2007:i:2:p:548-573

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Web page: http://www.elsevier.com/locate/jeconom

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  1. 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.
  2. Paulo M.M. Rodrigues & A.M. Robert Taylor, 2004. "Efficient Tests of the Seasonal Unit Root Hypothesis," Economics Working Papers ECO2004/29, European University Institute.
  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. J. Breitung & P. H. Franses, 1996. "On Phillips-Perron Type Tests for Seasonal Unit Roots," SFB 373 Discussion Papers 1996,27, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  5. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  6. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882, October.
  7. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
  8. 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.
  9. J. Joseph Beaulieu & Jeffrey A. Miron, 1992. "Seasonal Unit Roots in Aggregate U.S. Data," NBER Technical Working Papers 0126, National Bureau of Economic Research, Inc.
  10. 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 1057-72, June.
  11. 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(03), pages 269-306, September.
  12. 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 374-79, July.
  13. Smith, R.J. & Taylor, R., 1995. "Additional Critical Values and Asymptotic Representations for Seasonal Unit Roots Tests," Cambridge Working Papers in Economics 9529, Faculty of Economics, University of Cambridge.
  14. 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(04), pages 645-670, August.
  15. 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.
  16. 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.
  17. Rodrigues, Paulo M.M., 2001. "Near Seasonal Integration," Econometric Theory, Cambridge University Press, vol. 17(01), pages 70-86, February.
  18. 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 257-87, August.
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Citations

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Cited by:
  1. Anton Skrobotov, 2013. "On GLS-detrending for deterministic seasonality testing," Working Papers 0073, Gaidar Institute for Economic Policy, revised 2014.
  2. Paulo M.M. Rodrigues & A.M. Robert Taylor, . "Efficient Tests of the Seasonal Unit Root Hypothesis," Discussion Papers 06/12, University of Nottingham, School of Economics.
  3. Tomás del Barrio Castro & Denise R. Osborn & A.M. Robert Taylor, 2011. "On Augmented HEGY Tests for Seasonal Unit Roots," The School of Economics Discussion Paper Series 1121, Economics, The University of Manchester.
  4. 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.
  5. 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.
  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. Tomas del Barrio Castro & Mariam Camarero & Cecilio Tamarit, 2013. "An analysis of the trade balance for OECD countries using periodic integration and cointegration," Working Papers 1320, Department of Applied Economics II, Universidad de Valencia.

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