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Segmenting mean-nonstationary time series via trending regressions

Author

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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.

Suggested Citation

  • Aue, Alexander & Horváth, Lajos & Hušková, Marie, 2012. "Segmenting mean-nonstationary time series via trending regressions," Journal of Econometrics, Elsevier, vol. 168(2), pages 367-381.
  • Handle: RePEc:eee:econom:v:168:y:2012:i:2:p:367-381
    DOI: 10.1016/j.jeconom.2012.02.003
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    References listed on IDEAS

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    1. 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.
    2. Ghysels, Eric & Perron, Pierre, 1996. "The effect of linear filters on dynamic time series with structural change," Journal of Econometrics, Elsevier, vol. 70(1), pages 69-97, January.
    3. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    4. Ghysels, Eric & Guay, Alain & Hall, Alastair, 1998. "Predictive tests for structural change with unknown breakpoint," Journal of Econometrics, Elsevier, vol. 82(2), pages 209-233, February.
    5. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    6. Alexander Aue & Lajos Horváth & Marie Hušková & Piotr Kokoszka, 2006. "Change-point monitoring in linear models," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 373-403, November.
    7. Koop, Gary & Potter, Simon, 2010. "A flexible approach to parametric inference in nonlinear and time varying time series models," Journal of Econometrics, Elsevier, vol. 159(1), pages 134-150, November.
    8. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    9. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
    10. Elena Andreou & Eric Ghysels, 2002. "Detecting multiple breaks in financial market volatility dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 579-600.
    11. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
    12. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    13. 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.
    14. Donald W. K. Andrews & C. John McDermott, 1995. "Nonlinear Econometric Models with Deterministically Trending Variables," Review of Economic Studies, Oxford University Press, vol. 62(3), pages 343-360.
    15. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    16. 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.
    17. 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.
    18. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    19. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
    20. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
    21. repec:hal:journl:peer-00732535 is not listed on IDEAS
    22. Andreou, Elena, 2008. "Restoring monotone power in the CUSUM test," Economics Letters, Elsevier, vol. 98(1), pages 48-58, January.
    23. 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.
    24. 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.
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    Citations

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    Cited by:

    1. Chihwa Kao & Lorenzo Trapani & Giovanni Urga, 2012. "Testing for Instability in Covariance Structures," Center for Policy Research Working Papers 131, Center for Policy Research, Maxwell School, Syracuse University.
    2. 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;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.

    More about this item

    Keywords

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

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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