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

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  • 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.

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Bibliographic Info

Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 056.

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Date of creation: 2011
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Handle: RePEc:unm:umamet:2011056

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Keywords: econometrics;

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  1. Smeekes, Stephan & Taylor, A.M. Robert, 2012. "Bootstrap Union Tests For Unit Roots In The Presence Of Nonstationary Volatility," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 28(02), pages 422-456, April.
  2. 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, Department of Economics, University of Oxford, vol. 67(1), pages 115-134, 02.
  3. Patrick Richard, 2008. "Modified Fast Double Sieve Bootstraps for ADF Tests," Cahiers de recherche, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke 08-17, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke.
  4. M Sensier & D van Dijk, 2003. "Testing for Volatility Changes in US Macroeconomic Time Series," Centre for Growth and Business Cycle Research Discussion Paper Series, Economics, The Univeristy of Manchester 36, Economics, The Univeristy of Manchester.
  5. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 140(2), pages 919-947, October.
  6. van Dijk, D.J.C. & Osborn, D.R. & Sensier, M., 2002. "Changes in variability of the business cycle in the G7 countries," Econometric Institute Research Papers, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute EI 2002-28, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  7. Pierre Perron & Zhongjun Qu, 2006. "A Simple Modification to Improve the Finite Sample Properties of Ng and Perron’s Unit Root Tests," Boston University - Department of Economics - Working Papers Series, Boston University - Department of Economics WP2006-010, Boston University - Department of Economics.
  8. Brendan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Papers 2008-W06, Economics Group, Nuffield College, University of Oxford.
  9. Margaret M. McConnell & Gabriel Perez Quiros, 1997. "Output fluctuations in the United States: what has changed since the early 1980s?," Research Paper, Federal Reserve Bank of New York 9735, Federal Reserve Bank of New York.
  10. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, Econometric Society, vol. 69(6), pages 1519-1554, November.
  11. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2009. "Heteroskedastic Time Series With A Unit Root," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 25(05), pages 1228-1276, October.
  12. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, Econometric Society, vol. 64(4), pages 813-36, July.
  13. Giuseppe Cavaliere & A. M. Robert Taylor, 2009. "Bootstrap M Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 28(5), pages 393-421.
  14. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 21(4), pages 431-447.
  15. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, Econometric Society, vol. 48(4), pages 817-38, May.
  16. Brandan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Series Working Papers, University of Oxford, Department of Economics 2008-WO6, University of Oxford, Department of Economics.
  17. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Bootstrap Unit Root Tests For Time Series With Nonstationary Volatility," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(01), pages 43-71, February.
  18. Xu, Ke-Li & Phillips, Peter C. B., 2011. "Tilted Nonparametric Estimation of Volatility Functions With Empirical Applications," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 29(4), pages 518-528.
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Cited by:
  1. Joakim Westerlund, . "Heteroskedasticity Robust Panel Unit Root tests," Financial Econometics Series, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance 2014_02, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.

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