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On LM-Type Tests for Seasonal Unit Roots in the Presence of a Break in Trend

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  • Luís Catela Nunes
  • Paulo M.M. Rodrigues

Abstract

This paper proposes tests for seasonal unit roots allowing for the presence of a break in the trend slope occurring at an unknown date. In particular, new LM type tests are derived based on the framework introduced by Hylleberg, Engle, Granger and Yoo [HEGY] (1990). Null asymptotic distributions are derived for the no break case as well as when a break is present in the data generating process. A Monte Carlo investigation on the finite sample size and power performance of the new procedures is presented.

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Bibliographic Info

Paper provided by Banco de Portugal, Economics and Research Department in its series Working Papers with number w200920.

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Date of creation: 2009
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Handle: RePEc:ptu:wpaper:w200920

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  1. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  2. Vogelsang, Timothy J & Perron, Pierre, 1998. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1073-1100, November.
  3. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-43, September.
  4. Ahn, Sung K. & Cho, Sinsup, 1993. "Some tests for unit roots in seasonal time series with deterministic trends," Statistics & Probability Letters, Elsevier, vol. 16(2), pages 85-95, January.
  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 374-79, July.
  6. Peter C.B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Cowles Foundation Discussion Papers 1189, Cowles Foundation for Research in Economics, Yale University.
  7. Smith, R.J. & Taylor, A.M.R., 1999. "Regression-Based Seasonal Unit Root Tests," Discussion Papers 99-15, Department of Economics, University of Birmingham.
  8. 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.
  9. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521562607.
  10. 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.
  11. 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.
  12. Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
  13. Perron, P., 1990. "Further Evidence On Breaking Trend Functions In Macroeconomics Variables," Papers 350, Princeton, Department of Economics - Econometric Research Program.
  14. Mohitosh Kejriwal & Pierre Perron, 2006. "Unit Root Tests Allowing for a Break in the Trend Function at an Unknown Time Under Both the Null and Alternative Hypotheses," Boston University - Department of Economics - Working Papers Series WP2006-052, Boston University - Department of Economics.
  15. Hassler, Uwe & Rodrigues, Paulo M. M., 2002. "Seasonal Unit Root Tests under Structural Breaks," Darmstadt Discussion Papers in Economics 37696, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute of Economics (VWL).
  16. 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.
  17. Harvey, David I. & Leybourne, Stephen J. & Newbold, Paul, 2002. "Seasonal unit root tests with seasonal mean shifts," Economics Letters, Elsevier, vol. 76(2), pages 295-302, July.
  18. Philip Hans Franses & Timothy J. Vogelsang, 1998. "On Seasonal Cycles, Unit Roots, And Mean Shifts," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 231-240, May.
  19. Nunes, Luis C. & Kuan, Chung-Ming & Newbold, Paul, 1995. "Spurious Break," Econometric Theory, Cambridge University Press, vol. 11(04), pages 736-749, August.
  20. 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.
  21. 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.
  22. Eric Ghysels & Denise R. Osborn & Paulo M. M. Rodrigues, 1999. "Seasonal Nonstationarity and Near-Nonstationarity," CIRANO Working Papers 99s-05, CIRANO.
  23. 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.
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Cited by:
  1. Junsoo Lee & Mark C. Strazicich, 2013. "Minimum LM unit root test with one structural break," Economics Bulletin, AccessEcon, vol. 33(4), pages 2483-2492.

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