On the limiting behaviour of augmented seasonal unit root tests
In a recent paper, Taylor (2003) has shown that the seasonal unit root tests of Dickey et al. (1984) [DHF] have non-degenerate limiting distributions for series which admit unit roots at any of the zero or seasonal frequencies. In this note we go a stage further and show that the standard practice of augmenting the DHF regression with lagged dependent variables alters the limiting distributions of the DHF statistics in the above scenario. Associated Monte Carlo evidence shows that this may either increase or decrease (possibly even below the nominal level) the rejection frequencies of the tests, relative to the unaugmented case.
Volume (Year): 3 (2005)
Issue (Month): 3 ()
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- Taylor, A.M. Robert, 2003. "On The Asymptotic Properties Of Some Seasonal Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(02), pages 311-321, April.
- Hylleberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988.
"Seasonal, Integration And Cointegration,"
6-88-2, Pennsylvania State - Department of Economics.
- Smith, Richard J. & Taylor, A.M. Robert & del Barrio Castro, Tomas, 2009.
"Regression-Based Seasonal Unit Root Tests,"
Cambridge University Press, vol. 25(02), pages 527-560, April.
- Richard J. Smith & A. M. Robert Taylor & Tomas del Barrio Castro, 2007. "Regression-based seasonal unit root tests," Discussion Papers 07/05, University of Nottingham, Granger Centre for Time Series Econometrics.
- Smith, R.J. & Taylor, A.M.R., 1999. "Regression-Based Seasonal Unit Root Tests," Discussion Papers 99-15, Department of Economics, University of Birmingham.
- 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.
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