Regression-Based Seasonal Unit Root Tests
The contribution of this paper is threefold. First, a characterization theorem of the subhypotheses comprising the seasonal unit root hypothesis is presented that provides a precise formulation of the alternative hypotheses associated with regression- based seasonal unit root tests. Second, it proposes regression-based tests for the seasonal unit root hypothesis that allow a general seasonal aspect for the data and are similar both exactly and asymptotically with respect to initial values and seasonal drift parameters. Third, 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 F -statistics 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 that is consonant with the predictions from the large-sample theory.
Volume (Year): 25 (2009)
Issue (Month): 02 (April)
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- 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.
- Ghysels,Eric & Osborn,Denise R., 2001.
"The Econometric Analysis of Seasonal Time Series,"
Cambridge University Press, number 9780521565882, November.
- 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.
- 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.
- Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
- 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.
- Engle, Robert F & Granger, Clive W J, 1987.
"Co-integration and Error Correction: Representation, Estimation, and Testing,"
Econometric Society, vol. 55(2), pages 251-76, March.
- Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
- J. Joseph Beaulieu & Jeffrey A. Miron, 1992.
"Seasonal Unit Roots in Aggregate U.S. Data,"
NBER Technical Working Papers
0126, National Bureau of Economic Research, Inc.
- 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.
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