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Robust methods for detecting multiple level breaks in autocorrelated time series

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  • David I. Harvey
  • Stephen J. Leybourne
  • A. M. Robert Taylor

Abstract

The contribution of this paper is twofold. First we extend the large sample results provided for the augmented Dickey-Fuller test by Said and Dickey (1984) and Chang and Park (2002) to the case of the augmented seasonal unit root tests of Hylleberg et al. (1990) [HEGY], inter alia. Our analysis is performed under the same conditions on the innovations as in Chang and Park (2002), thereby allowing for general linear processes driven by (possibly conditionally heteroskedastic) martingale difference innovations. We show that the limiting null distributions of the t-statistics for unit roots at the zero and Nyquist frequencies and joint F-type statistics are pivotal, while those of the t-statistics at the harmonic seasonal frequencies depend on nuisance parameters which derive from the lag parameters characterising the linear process. Moreover, the rates on the lag truncation required for these results to hold are shown to coincide with the corresponding rates given in Chang and Park (2002); in particular, an o(T 1/2) rate is shown to be sufficient. The second contribution of the paper is to explore the use of data-dependent lag selection methods in the context of the augmented HEGY tests. Information criteria based methods along with sequential rules, such as those of Ng and Perron (1995) and Beaulieu and Miron (1993), are compared.

Suggested Citation

  • David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2011. "Robust methods for detecting multiple level breaks in autocorrelated time series," Discussion Papers 11/01, University of Nottingham, Granger Centre for Time Series Econometrics.
  • Handle: RePEc:not:notgts:11/01
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    References listed on IDEAS

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    1. Pierre Perron & Gabriel RodrÌguez, 2003. "Searching For Additive Outliers In Nonstationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 193-220, March.
    2. Mohitosh Kejriwal & Pierre Perron, 2010. "A sequential procedure to determine the number of breaks in trend with an integrated or stationary noise component," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 305-328, September.
    3. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
    4. Bunzel, Helle & Vogelsang, Timothy J., 2005. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch-Singer Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 381-394, October.
    5. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
    6. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Estimating deterministic trends with an integrated or stationary noise component," Journal of Econometrics, Elsevier, vol. 151(1), pages 56-69, July.
    7. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
    8. 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.
    9. 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.
    10. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Testing for Shifts in Trend With an Integrated or Stationary Noise Component," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 369-396.
    11. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(03), pages 587-636, June.
    12. 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.
    13. Leisch, Friedrich & Hornik, Kurt & Kuan, Chung-Ming, 2000. "Monitoring Structural Changes With The Generalized Fluctuation Test," Econometric Theory, Cambridge University Press, vol. 16(06), pages 835-854, December.
    14. Peter Burridge & A. M. Robert Taylor, 2006. "Additive Outlier Detection Via Extreme-Value Theory," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 685-701, September.
    15. Perron, Pierre & Vogelsang, Timothy J, 1992. "Testing for a Unit Root in a Time Series with a Changing Mean: Corrections and Extensions," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 467-470, October.
    16. Sayginsoy, Özgen & Vogelsang, Timothy J., 2011. "Testing For A Shift In Trend At An Unknown Date: A Fixed-B Analysis Of Heteroskedasticity Autocorrelation Robust Ols-Based Tests," Econometric Theory, Cambridge University Press, vol. 27(05), pages 992-1025, October.
    17. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
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    Citations

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    Cited by:

    1. Claudio Morana, 2014. "Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks," Working Papers 273, University of Milano-Bicocca, Department of Economics, revised May 2014.
    2. 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.
    3. David Harvey & Stephen Leybourne, "undated". "Confidence sets for the date of a break in level and trend when the order of integration is unknown," Discussion Papers 14/04, University of Nottingham, Granger Centre for Time Series Econometrics.
    4. Nuno Sobreira & Luis C. Nunes & Paulo M. M. Rodrigues, 2014. "Characterizing Economic Growth Paths Based On New Structural Change Tests," Economic Inquiry, Western Economic Association International, vol. 52(2), pages 845-861, April.
    5. Mohitosh Kejriwal & Pierre Perron, 2010. "A sequential procedure to determine the number of breaks in trend with an integrated or stationary noise component," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 305-328, September.
    6. Mohitosh Kejriwal & Claude Lopez, 2013. "Unit Roots, Level Shifts, and Trend Breaks in Per Capita Output: A Robust Evaluation," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 892-927, November.
    7. Presno, María José & Landajo, Manuel & Fernández, Paula, 2012. "Non-renewable resource prices. A robust evaluation from the stationarity perspective," MPRA Paper 42523, University Library of Munich, Germany.
    8. Ghoshray, Atanu & Kejriwal, Mohitosh & Wohar, Mark E., 2011. "Breaking Trends and the Prebisch-Singer Hypothesis: A Further Investigation," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 120387, European Association of Agricultural Economists.
    9. Paulo M. M. Rodrigues, 2013. "Recursive adjustment, unit root tests and structural breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 62-82, January.
    10. Fabien CANDAU & Serge REY & Jean-François HOARAU & Michaël GOUJON, 2013. "Real exchange rate and competitiveness of an EU’s ultra-peripheral region: La Reunion Island," Working Papers 2013-2014_6, CATT - UPPA - Université de Pau et des Pays de l'Adour, revised Oct 2013.
    11. Ghoshray Atanu & Kejriwal Mohitosh & Wohar Mark, 2014. "Breaks, trends and unit roots in commodity prices: a robust investigation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(1), pages 23-40, February.
    12. Harvey, David I. & Leybourne, Stephen J., 2015. "Confidence sets for the date of a break in level and trend when the order of integration is unknown," Journal of Econometrics, Elsevier, vol. 184(2), pages 262-279.
    13. Anton Skrobotov, 2014. "A simple modification of the Busetti-Harvey stationarity tests with structural breaks at unknown time," Working Papers 0102, Gaidar Institute for Economic Policy, revised 2014.
    14. David I. Harvey & Stephen J. Leybourne, "undated". "Break date estimation for models with deterministic structural change," Discussion Papers 13/02, University of Nottingham, Granger Centre for Time Series Econometrics.
    15. Josep Lluís Carrion-i-Silvestre & Maria Dolores Gadea, 2015. "Testing for multiple level shifts in I(0) and I(1) stochastic processes," EcoMod2015 8702, EcoMod.
    16. Presno, María José & Landajo, Manuel & Fernández, Paula, 2014. "Non-renewable resource prices: A robust evaluation from the stationarity perspective," Resource and Energy Economics, Elsevier, vol. 36(2), pages 394-416.
    17. Sobreira, Nuno & Nunesz, Luis C. & Rodriguesz, Paulo M. M., 2012. "Neoclassical, semi-endogenous or endogenous growth theory? Evidence based on new structural change tests," Insper Working Papers wpe_291, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.

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