Regression-based seasonal unit root tests
AbstractThe contribution of this paper is three-fold. Firstly, a characterisation theorem of the sub-hypotheses comprising the seasonal unit root hypothesis is presented which provides a precise formulation of the alternative hypotheses against which regression-based seasonal unit root tests test. Secondly, it proposes regressionbased tests for the seasonal unit root hypothesis which allow a general seasonal aspect for the data and are similar both exactly and asymptotically with respect to initial values and seasonal drift parameters. Thirdly, limiting distribution theory is given for these statistics where, in contrast to previous papers in the literature, in doing so it is not assumed that unit roots hold at all of the zero and seasonal frequencies. This is shown to alter the large sample null distribution theory for regression t-statistics for unit roots at the complex frequencies, but interestingly to not affect the limiting null distributions of the regression t-statistics for unit roots at the zero and Nyquist frequencies and regression Fstatistics for unit roots at the complex frequencies. Our results therefore have important implications for how tests of the seasonal unit root hypothesis should be conducted in practice. Associated simulation evidence on the size and power properties of the statistics presented in this paper is given which is consonant with the predictions from the large sample theory.
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 University of Nottingham, Granger Centre for Time Series Econometrics in its series Discussion Papers with number 07/05.
Date of creation: Sep 2007
Date of revision:
Contact details of provider:
Postal: School of Economics University of Nottingham University Park Nottingham NG7 2RD
Phone: (44) 0115 951 5620
Fax: (0115) 951 4159
Web page: http://www.nottingham.ac.uk/economics/grangercentre/
More information through EDIRC
Seasonal unit root tests; seasonal drifts; characterisation theorem;
Other versions of this item:
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
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.:
- Hyllerberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988.
"Seasonal Integration And Cointegration,"
0-88-2, Pennsylvania State - Department of Economics.
- Joseph Beaulieu, J. & Miron, Jeffrey A., 1993.
"Seasonal unit roots in aggregate U.S. data,"
Journal of Econometrics,
Elsevier, vol. 55(1-2), pages 305-328.
- Burridge, Peter & Robert Taylor, A. M., 2004.
"Bootstrapping the HEGY seasonal unit root tests,"
Journal of Econometrics,
Elsevier, vol. 123(1), pages 67-87, November.
- Robert Taylor & Peter Burridge, 2004. "Bootstrapping the HEGY Seasonal Unit Root Tests," Econometric Society 2004 North American Summer Meetings 125, Econometric Society.
- Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
- Canova, Fabio & Hansen, Bruce E, 1995. "Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 237-52, July.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- Ghysels,Eric & Osborn,Denise R., 2001.
"The Econometric Analysis of Seasonal Time Series,"
Cambridge University Press, number 9780521562607, November.
- Ghysels, Eric & Lee, Hahn S. & Noh, Jaesum, 1994. "Testing for unit roots in seasonal time series : Some theoretical extensions and a Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 62(2), pages 415-442, June.
- Burridge, Peter & Taylor, A M Robert, 2001. "On the Properties of Regression-Based Tests for Seasonal Unit Roots in the Presence of Higher-Order Serial Correlation," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 374-79, July.
- Robert Taylor & Peter Burridge, 2004.
"Bootstrapping the HEGY Seasonal Unit Root Tests,"
Econometric Society 2004 North American Summer Meetings
125, Econometric Society.
- 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,"
056, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- Giuseppe Cavaliere & Peter C.B. Phillips & Stephan Smeekes & A.M. Robert Taylor, 2012. "Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility," Cowles Foundation Discussion Papers 1844, Cowles Foundation for Research in Economics, Yale University.
- Denise Osborn & Paulo Rodrigues, 2002. "Asymptotic Distributions Of Seasonal Unit Root Tests: A Unifying Approach," Econometric Reviews, Taylor and Francis Journals, vol. 21(2), pages 221-241.
- Niels Haldrup & Antonio Montanés & Andreu Sanso, .
"Measurement Errors and Outliers in Seasonal Unit Root Testing,"
Economics Working Papers
2000-8, School of Economics and Management, University of Aarhus.
- Haldrup, Niels & Montanes, Antonio & Sanso, Andreu, 2005. "Measurement errors and outliers in seasonal unit root testing," Journal of Econometrics, Elsevier, vol. 127(1), pages 103-128, July.
- Haldrup, Niels Prof. & Montanes, Antonio & SansÃ³, Andreu, 2000. "Measurement Errors and Outliers in Seasonal Unit Root Testing," University of California at San Diego, Economics Working Paper Series qt0gw7q9hk, Department of Economics, UC San Diego.
- Luís Catela Nunes & Paulo M.M. Rodrigues, 2009.
"On LM-Type Tests for Seasonal Unit Roots in the Presence of a Break in Trend,"
w200920, Banco de Portugal, Economics and Research Department.
- Luis C. Nunes & Paulo M. M. Rodrigues, 2011. "On LM‐type tests for seasonal unit roots in the presence of a break in trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 108-134, 03.
- Uwe Hassler & Paulo M. M. Rodrigues, 2004.
"Seasonal Unit Root Tests Under Structural Breaks,"
Journal of Time Series Analysis,
Wiley Blackwell, vol. 25(1), pages 33-53, 01.
- Castro, Tomás del Barrio & Osborn, Denise R. & Taylor, A.M. Robert, 2012.
"On Augmented Hegy Tests For Seasonal Unit Roots,"
Cambridge University Press, vol. 28(05), pages 1121-1143, October.
- repec:dar:vpaper:37696 is not listed on IDEAS
- Robert Taylor, 2005. "On the limiting behaviour of augmented seasonal unit root tests," Economics Bulletin, AccessEcon, vol. 3(3), pages 1-10.
- Tomas del Barrio Castro, 2007.
"Using the HEGY Procedure When Not All Roots Are Present,"
Working Papers in Economics
170, Universitat de Barcelona. Espai de Recerca en Economia.
- Tomas del Barrio Castro, 2007. "Using the HEGY Procedure When Not All Roots Are Present," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(6), pages 910-922, November.
- Olivier Darné & Claude Diebolt, 2002. "A Note on Seasonal Unit Root Tests," Quality & Quantity: International Journal of Methodology, Springer, vol. 36(3), pages 305-310, August.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().
If references are entirely missing, you can add them using this form.