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Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility

Author

Listed:
  • Cavaliere Giuseppe
  • Phillips Peter C.B.
  • Smeekes Stephan
  • Taylor A.M. Robert

    (METEOR)

Abstract

A number of recently published papers have focused on the problem of testing for a unit root inthe case where the driving shocks may be unconditionally heteroskedastic. These papers have,however, assumed that the lag length in the unit root test regression is a deterministic functionof the sample size, rather than data-determined, the latter being standard empirical practice. Inthis paper we investigate the finite sample impact of unconditional heteroskedasticity onconventional data-dependent methods of lag selection in augmented Dickey-Fuller type unit roottest regressions and propose new lag selection criteria which allow for the presence ofheteroskedasticity in the shocks. We show that standard lag selection methods show a tendency toover-fit the lag order under heteroskedasticity, which results in significant power losses in the(wild bootstrap implementation of the) augmented Dickey-Fuller tests under the alternative. Thenew lag selection criteria we propose are shown to avoid this problem yet deliver unit root testswith almost identical finite sample size and power properties as the corresponding tests based onconventional lag selection methods when the shocks are homoskedastic.

Suggested Citation

  • Cavaliere Giuseppe & Phillips Peter C.B. & Smeekes Stephan & Taylor A.M. Robert, 2011. "Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2011056
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    References listed on IDEAS

    as
    1. Marianne Sensier & Dick van Dijk, 2004. "Testing for Volatility Changes in U.S. Macroeconomic Time Series," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 833-839, August.
    2. Richard, Patrick, 2009. "Modified fast double sieve bootstraps for ADF tests," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4490-4499, October.
    3. Ke-Li Xu & Peter C. B. Phillips, 2011. "Tilted Nonparametric Estimation of Volatility Functions With Empirical Applications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 518-528, October.
    4. Giuseppe Cavaliere & A. M. Robert Taylor, 2009. "Bootstrap M Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 393-421.
    5. 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.
    6. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2009. "Heteroskedastic Time Series With A Unit Root," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1228-1276, October.
    7. Smeekes, Stephan & Taylor, A.M. Robert, 2012. "Bootstrap Union Tests For Unit Roots In The Presence Of Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 28(02), pages 422-456, April.
    8. Brendan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Papers 2008-W06, Economics Group, Nuffield College, University of Oxford.
    9. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
    10. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    11. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-783, August.
    12. 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.
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    14. Perron, Pierre & Qu, Zhongjun, 2007. "A simple modification to improve the finite sample properties of Ng and Perron's unit root tests," Economics Letters, Elsevier, vol. 94(1), pages 12-19, January.
    15. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    16. Margaret M. McConnell & Gabriel Perez-Quiros, 2000. "Output fluctuations in the United States: what has changed since the early 1980s?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    17. Brandan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Series Working Papers 2008-WO6, University of Oxford, Department of Economics.
    18. 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.
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    Cited by:

    1. repec:spr:agfoec:v:5:y:2017:i:1:d:10.1186_s40100-017-0074-0 is not listed on IDEAS
    2. Yuriy Gorodnichenko & Tho Pham & Oleksandr Talavera, 2018. "Social Media, Sentiment and Public Opinions: Evidence from #Brexit and #USElection," NBER Working Papers 24631, National Bureau of Economic Research, Inc.
    3. repec:eee:joecas:v:12:y:2015:i:2:p:153-161 is not listed on IDEAS
    4. Xu, Bin & Lin, Boqiang, 2016. "Reducing CO2 emissions in China's manufacturing industry: Evidence from nonparametric additive regression models," Energy, Elsevier, vol. 101(C), pages 161-173.
    5. Smeekes S. & Urbain J.R.Y.J., 2014. "A multivariate invariance principle for modified wild bootstrap methods with an application to unit root testing," Research Memorandum 008, Maastricht University, Graduate School of Business and Economics (GSBE).
    6. Skrobotov Anton & Cavaliere Giuseppe & Taylor Robert, 2016. "Wild Bootstrap Seasonal Unit Root Tests for Time Series with Periodic Non-Stationary Volatility," Working Papers wpaper-2016-269, Gaidar Institute for Economic Policy, revised 2016.

    More about this item

    Keywords

    econometrics;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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