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Data-Dependent Methods for the Lag Length Selection in Unit Root Tests with Structural Change

Author

Listed:
  • Ricardo Quineche Uribe

    ( Banco Central de la Reserva del Perú)

  • Gabriel Rodríguez

    ( Departamento de Economía de la Pontificia Universidad Católica del Perú)

Abstract

We analyze the choice of the truncation lag for unit root tests as the ADF(GLS) and the M(GLS) tests proposed by Elliott et al. (1996) and Ng and Perron (2001) and extended to the context of structural change by Perron and RodrÌguez (2003). We consider the models that allows for a change in slope and a change in the intercept and slope at unknown break date, respectively. Using Monte-Carlo experiments, the truncation lag selected according to several methods as the AIC, BIC, M(AIC), MBIC is analyzed. We also include and analyze the performance of the hybrid version suggested by Perron and Qu (2007) which uses OLS instead of GLS detrended data when constructing the information criteria. All these methods are compared to the sequential t-sig method based on testing for the signiÖcance of coe¢ cients on additional lags in the ADF autoregression. Results show that the MGLS tests present explosive values associated with large values of the lag selected which happens more often when AIC, AIC(OLS) and t-sig are used to select the lag length. The values are so negative that imply an over rejection of the null hypothesis of a unit root. On the opposite side, lag length selected using M(AIC), M(AICOLS), M(BIC), M(BICOLS) methods lead to very small values of the M-tests implying very conservative results, that is, no rejection of the null hypothesis. These opposite power problems are not observed in the case of the ADF(GLS) test for which it is highly recommended. JEL Classification-JEL: C22, C52

Suggested Citation

  • Ricardo Quineche Uribe & Gabriel Rodríguez, 2015. "Data-Dependent Methods for the Lag Length Selection in Unit Root Tests with Structural Change," Documentos de Trabajo / Working Papers 2015-404, Departamento de Economía - Pontificia Universidad Católica del Perú.
    • Handle: RePEc:pcp:pucwps:wp00404
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    References listed on IDEAS

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    1. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 435-463.
    2. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots," NBER Chapters, in: NBER Macroeconomics Annual 1991, Volume 6, pages 141-220, National Bureau of Economic Research, Inc.
    3. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    4. Perron, Pierre, 1997. "Further evidence on breaking trend functions in macroeconomic variables," Journal of Econometrics, Elsevier, vol. 80(2), pages 355-385, October.
    5. Serena Ng & Pierre Perron, 2005. "A Note on the Selection of Time Series Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(1), pages 115-134, February.
    6. Perron, Pierre & Ng, Serena, 1998. "An Autoregressive Spectral Density Estimator At Frequency Zero For Nonstationarity Tests," Econometric Theory, Cambridge University Press, vol. 14(5), pages 560-603, October.
    7. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
    8. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    9. 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.
    10. Agiakloglou, Christos & Newbold, Paul, 1996. "The balance between size and power in Dickey-Fuller tests with data-dependent rules for the choice of truncation lag," Economics Letters, Elsevier, vol. 52(3), pages 229-234, September.
    11. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    12. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 369-384.
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    1. Ricardo Quineche & Gabriel Rodríguez, 2017. "Selecting the Lag Length for the M GLS Unit Root Tests with Structural Change: A Warning Note for Practitioners Based on Simulations," Econometrics, MDPI, vol. 5(2), pages 1-10, April.

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    More about this item

    Keywords

    Unit Root Tests; Structural Change; Truncation Lag; GLS Detrending; Information Criteria; Sequential General to SpeciÖc t-sig Method.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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