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Testing For A Shift In Trend At An Unknown Date: A Fixed-B Analysis Of Heteroskedasticity Autocorrelation Robust Ols-Based Tests

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  • Sayginsoy, Özgen
  • Vogelsang, Timothy J.

Abstract

This paper analyzes tests for a shift in the trend function of a time series at an unknown date based on ordinary least squares (OLS) estimates of the trend function. Inference about the trend parameters depends on the serial correlation structure of the data through the long-run variance (zero frequency spectral density) of the errors. Asymptotically pivotal tests can be obtained by the use of serial correlation robust standard errors that require an estimate of the long-run variance. The focus is on the class of nonparametric kernel estimators of the long-run variance. Tests based on these estimators present two problems for practitioners. The first is the choice of kernel and bandwidth. The second is the well-known overrejection problem caused by strong serial correlation (or a possible unit root) in the errors.We provide solutions to both problems by using the fixed- b asymptotic framework of Kiefer and Vogelsang (2005, Econometric Theory , 21, 1130–1164) in conjunction with the scaling factor approach of Vogelsang (1998, Econometrica 65, 123–148). Our results provide practitioners with a family of OLS-based trend function structural change tests that are size robust to the presence of strong serial correlation or a unit root. Specific recommendations are provided for the tuning parameters (kernel and bandwidth) in a way that maximizes asymptotic integrated power.

Suggested Citation

  • 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.
  • Handle: RePEc:cup:etheor:v:27:y:2011:i:05:p:992-1025_00
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    Cited by:

    1. Abi Morshed, Alaa & Andreou, E. & Boldea, Otilia, 2016. "Structural Break Tests Robust to Regression Misspecification," Discussion Paper 2016-019, Tilburg University, Center for Economic Research.
    2. Fabrizio Iacone & Stephen J. Leybourne & A. M. Robert Taylor, 2014. "A FIXED- b TEST FOR A BREAK IN LEVEL AT AN UNKNOWN TIME UNDER FRACTIONAL INTEGRATION," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 40-54, January.
    3. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2010. "Robust methods for detecting multiple level breaks in autocorrelated time series," Journal of Econometrics, Elsevier, vol. 157(2), pages 342-358, August.
    4. YAMAZAKI, Daisuke & KUROZUMI, Eiji, 2014. "Improving the Finite Sample Performance of Tests for a Shift in Mean," Discussion Papers 2014-16, Graduate School of Economics, Hitotsubashi University.
    5. Seong Yeon Chang & Pierre Perron, 2016. "Inference on a Structural Break in Trend with Fractionally Integrated Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 555-574, July.
    6. 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.
    7. David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2009. "Robust methods for detecting multiple level breaks in autocorrelated time series [Revised to become No. 10/01 above]," Discussion Papers 09/01, University of Nottingham, Granger Centre for Time Series Econometrics.
    8. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.

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