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A Sequential Procedure to Determine the Number of Breaks in Trend with an Integrated or Stationary Noise Component

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  • Mohitosh Kejriwal
  • Pierre Perron

Abstract

Perron and Yabu (2008) consider the problem of testing for a break occuring at an unknown date in the trend function of a univariate time series when the noise component can be either stationary or integrated. This paper extends their work by proposing a sequential test that allows one to test the null hypothesis of, say, l breaks, versus the alternative hypothesis of (l + 1) breaks. The test enables consistent estimation of the number of breaks. In both stationary and integrated cases, it is shown that asymptotic critical values can be obtained from the relevant quantiles of the limit distribution of the test for a single break. Monte Carlo simulations suggest that the procedure works well in finite samples.

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Bibliographic Info

Paper provided by Purdue University, Department of Economics in its series Purdue University Economics Working Papers with number 1217.

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Length: 25 pages
Date of creation: Feb 2009
Date of revision:
Handle: RePEc:pur:prukra:1217

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Keywords: structural change; sequential procedure; feasible gls; unit root; structural breaks;

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References

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  1. Kejriwal, Mohitosh & Perron, Pierre, 2008. "The limit distribution of the estimates in cointegrated regression models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 146(1), pages 59-73, September.
  2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  3. Kejriwal, Mohitosh & Lopez, Claude, 2010. "Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation," MPRA Paper 25204, University Library of Munich, Germany.
  4. Pierre Perron & Tomoyoshi Yabu, 2007. "Estimating Deterministic Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2007-020, Boston University - Department of Economics.
  5. BAI, Jushan & PERRON, Pierre, 1998. "Computation and Analysis of Multiple Structural-Change Models," Cahiers de recherche 9807, Universite de Montreal, Departement de sciences economiques.
  6. Kim, Dukpa & Perron, Pierre, 2009. "Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses," Journal of Econometrics, Elsevier, vol. 148(1), pages 1-13, January.
  7. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  8. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  9. Robin L. Lumsdaine & David H. Papell, 1997. "Multiple Trend Breaks And The Unit-Root Hypothesis," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 212-218, May.
  10. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  11. Ben-David, D., 1998. "Some Evidence on the Continuity of the Growth Process Among the G7 Countries," Papers 98-01, Houston - Department of Economics.
  12. Pierre Perron & Tomoyoshi Yabu, 2007. "Testing for Shifts in Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2007-025, Boston University - Department of Economics.
  13. Ben-David, Dan & Papell, David H., 1997. "International trade and structural change," Journal of International Economics, Elsevier, vol. 43(3-4), pages 513-523, November.
  14. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Simple, Robust, And Powerful Tests Of The Breaking Trend Hypothesis," Econometric Theory, Cambridge University Press, vol. 25(04), pages 995-1029, August.
  15. Loewy, Michael B. & Papell, David H., 1996. "Are U.S. regional incomes converging? Some further evidence," Journal of Monetary Economics, Elsevier, vol. 38(3), pages 587-598, December.
  16. Josep Lluís Carrion-i-Silvestre & Dukpa Kim & Pierre Perron, 2007. "GLS-based unit root tests with multiple structural breaks both under the null and the alternative hypotheses," Boston University - Department of Economics - Working Papers Series wp2008-019, Boston University - Department of Economics.
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