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Segmenting mean-nonstationary time series via trending regressions

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  • Aue, Alexander
  • Horváth, Lajos
  • Hušková, Marie

Abstract

In this paper, we provide a segmentation procedure for mean-nonstationary time series. The segmentation is obtained by casting the problem into the framework of detecting structural breaks in trending regression models in which the regressors are generated by suitably smooth functions. As test statistics we propose to use the maximally selected likelihood ratio statistics and a related statistics based on partial sums of weighted residuals. The main theoretical contribution of the paper establishes the extreme value distribution of these statistics and their consistency. To circumvent the slow convergence to the extreme value limit, we propose to employ a version of the circular bootstrap. This procedure is completely data-driven and does not require knowledge of the time series structure. In an empirical part, we show in a simulation study and applications to air carrier traffic and S&P500 data that the finite sample performance is very satisfactory.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 168 (2012)
Issue (Month): 2 ()
Pages: 367-381

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Handle: RePEc:eee:econom:v:168:y:2012:i:2:p:367-381

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

Related research

Keywords: Change-point analysis; Circular bootstrap; Extreme value asymptotics; Gaussian processes; Gumbel distribution; Linear models; Polynomial regression; Resampling; Trending regression;

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References

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  1. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  2. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
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  4. Perron, P. & Ghysels, E., 1994. "The Effect of Linear Filters on Dynamic Time series with Structural Change," Cahiers de recherche 9425, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  6. Elena Andreou & Eric Ghysels, 2001. "Detecting Multiple Breaks in Financial Market Volatility Dynamics," University of Cyprus Working Papers in Economics 0202, University of Cyprus Department of Economics.
  7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  8. BAI, Jushan & PERRON, Pierre, 1998. "Computation and Analysis of Multiple Structural-Change Models," Cahiers de recherche 9807, Universite de Montreal, Departement de sciences economiques.
  9. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
  10. Aue, Alexander & Horvth, Lajos & Huskov, Marie, 2009. "Extreme value theory for stochastic integrals of Legendre polynomials," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 1029-1043, May.
  11. Alexander Aue & Lajos Horv�th & Marie Hušková & Piotr Kokoszka, 2006. "Change-point monitoring in linear models," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 373-403, November.
  12. Donald W.K. Andrews & C. John McDermott, 1993. "Nonlinear Econometric Models with Deterministically Trending Variables," Cowles Foundation Discussion Papers 1053, Cowles Foundation for Research in Economics, Yale University.
  13. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
  14. Altissimo, Filippo & Corradi, Valentina, 2003. "Strong rules for detecting the number of breaks in a time series," Journal of Econometrics, Elsevier, vol. 117(2), pages 207-244, December.
  15. 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.
  16. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
  17. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
  18. Andreou, Elena, 2008. "Restoring monotone power in the CUSUM test," Economics Letters, Elsevier, vol. 98(1), pages 48-58, January.
  19. Dennis, Benjamin N. & Iscan, Talan B., 2009. "Engel versus Baumol: Accounting for structural change using two centuries of U.S. data," Explorations in Economic History, Elsevier, vol. 46(2), pages 186-202, April.
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Cited by:
  1. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 23(2), pages 219-255, June.

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