Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility
AbstractA number of recently published papers have focused on the problem of testing for a unit root in the 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 function of the sample size, rather than data-determined, the latter being standard empirical practice. In this paper we investigate the finite sample impact of unconditional heteroskedasticity on conventional data-dependent methods of lag selection in augmented Dickey-Fuller type unit root test regressions and propose new lag selection criteria which allow for the presence of heteroskedasticity in the shocks. We show that standard lag selection methods show a tendency to over-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. The new lag selection criteria we propose are shown to avoid this problem yet deliver unit roots with almost identical finite sample size and power properties as the corresponding tests based on conventional lag selection methods when the shocks are homoskedastic.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1844.
Length: 35 pages
Date of creation: Jan 2012
Date of revision:
Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
Other versions of this item:
- 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).
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-01-18 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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
36, Economics, The Univeristy of Manchester.
- 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.
- 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, 02.
- 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.
- Margaret M. McConnell & Gabriel Perez Quiros, 1998.
"Output fluctuations in the United States: what has changed since the early 1980s?,"
41, Federal Reserve Bank of New York.
- Margaret 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.
- Gabriel Perez-Quiros & Margaret M. McConnell, 2000. "Output Fluctuations in the United States: What Has Changed since the Early 1980's?," American Economic Review, American Economic Association, vol. 90(5), pages 1464-1476, December.
- Margaret M. McConnell & Gabriel Perez Quiros, 1997. "Output fluctuations in the United States: what has changed since the early 1980s?," Research Paper 9735, Federal Reserve Bank of New York.
- D van Dijk & D R Osborn & M Sensier, 2002.
"Changes in variability of the business cycle in the G7 countries,"
The School of Economics Discussion Paper Series
0204, Economics, The University of Manchester.
- 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 EI 2002-28, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- D van Dijk & D R Osborn & M Sensier, 2002. "Changes in Variability of the Business Cycle in the G7 Countries," Centre for Growth and Business Cycle Research Discussion Paper Series 16, Economics, The Univeristy of Manchester.
- Patrick Richard, 2008.
"Modified Fast Double Sieve Bootstraps for ADF Tests,"
Cahiers de recherche
08-17, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke.
- Richard, Patrick, 2009. "Modified fast double sieve bootstraps for ADF tests," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4490-4499, October.
- Brendan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Papers 2008-W06, Economics Group, Nuffield College, University of Oxford.
- Perron, Pierre & Qu, Zhongjun, 2007.
"A simple modification to improve the finite sample properties of Ng and Perron's unit root tests,"
Elsevier, vol. 94(1), pages 12-19, January.
- 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 WP2006-010, Boston University - Department of Economics.
- 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.
- Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992.
"Efficient Tests for an Autoregressive Unit Root,"
NBER Technical Working Papers
0130, National Bureau of Economic Research, Inc.
- Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
- Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Bootstrap Unit Root Tests For Time Series With Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 24(01), pages 43-71, February.
- Serena Ng & Pierre Perron, 1997.
"Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power,"
Boston College Working Papers in Economics
369, Boston College Department of Economics, revised 01 Sep 2000.
- 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.
- 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, vol. 29(4), pages 518-528.
- Giuseppe Cavaliere & A. M. Robert Taylor, 2009. "Bootstrap M Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 393-421.
- White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
- Smeekes Stephan & Taylor A. M. Robert, 2010.
"Bootstrap Union Tests for Unit Roots in the Presence of Nonstationary Volatility,"
015, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- 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.
- Stephan Smeekes & A. M. Robert Taylor, 2010. "Bootstrap union tests for unit roots in the presence of nonstationary volatility," Discussion Papers 10/03, University of Nottingham, Granger Centre for Time Series Econometrics.
- Brandan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Series Working Papers 2008-WO6, University of Oxford, Department of Economics.
- Joakim Westerlund, . "Heteroskedasticity Robust Panel Unit Root tests," Financial Econometics Series 2014_02, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Glena Ames).
If references are entirely missing, you can add them using this form.