Using the HEGY Procedure When Not All Roots Are Present
Empirical studies have shown little evidence to support the presence of all unit roots present in the Delta_4 filter in quarterly seasonal time series. This paper analyses the performance of the Hylleberg, Engle, Granger and Yoo [Journal of Econometrics (1990) Vol. 44, pp. 215-238] (HEGY) procedure when the roots under the null are not all present. We exploit the vector of quarters representation and cointegration relationship between the quarters when factors (1 - L), (1 + L), (1 + L-super-2), (1 - L-super-2) and (1 + L + L-super-2 + L-super-3) are a source of nonstationarity in a process in order to obtain the distribution of tests of the HEGY procedure when the underlying processes have a root at the zero, Nyquist frequency, two complex conjugates of frequency pi/2 and two combinations of the previous cases. We show both theoretically and through a Monte Carlo analysis that the t-ratios t and t and the F-type tests used in the HEGY procedure have the same distribution as under the null of a seasonal random walk when the root(s) is (are) present, although this is not the case for the t-ratio tests associated with unit roots at frequency pi/2. Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.
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Volume (Year): 28 (2007)
Issue (Month): 6 (November)
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- Smith, R.J. & Taylor, A.M.R., 1999.
"Regression-Based Seasonal Unit Root Tests,"
99-15, Department of Economics, University of Birmingham.
- Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990.
"Seasonal integration and cointegration,"
Journal of Econometrics,
Elsevier, vol. 44(1-2), pages 215-238.
- Hyllerberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988. "Seasonal Integration And Cointegration," Papers 0-88-2, Pennsylvania State - Department of Economics.
- Hylleberg, S. & Engle, R.F. & Granger, C.W.J. & Yoo, B.S., 1988. "Seasonal, Integration And Cointegration," Papers 6-88-2, Pennsylvania State - Department of Economics.
- Denise Osborn & Paulo Rodrigues, 2002. "Asymptotic Distributions Of Seasonal Unit Root Tests: A Unifying Approach," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 221-241.
- Phillips, Peter C B & Ouliaris, S, 1990.
"Asymptotic Properties of Residual Based Tests for Cointegration,"
Econometric Society, vol. 58(1), pages 165-93, January.
- Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
- Tom Doan, . "POTESTRESIDS: RATS procedure to perform Phillips-Ouliaris-Hansen test for Cointegration on 1st stage residuals," Statistical Software Components RTS00248, Boston College Department of Economics.
- Tom Doan, . "POTEST: RATS procedure to perform Phillips-Ouliaris-Hansen test for Cointegration," Statistical Software Components RTS00247, Boston College Department of Economics.
- 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.
- Hylleberg, Svend & Jorgensen, Clara & Sorensen, Nils Karl, 1993. "Seasonality in Macroeconomic Time Series," Empirical Economics, Springer, vol. 18(2), pages 321-35.
- 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.
- Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2004. "Asymptotic Distributions For Regression-Based Seasonal Unit Root Test Statistics In A Near-Integrated Model," Econometric Theory, Cambridge University Press, vol. 20(04), pages 645-670, August.
- Castro, Tomas del Barrio & Osborn, Denise R., 2008. "Testing For Seasonal Unit Roots In Periodic Integrated Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 24(04), pages 1093-1129, August.
- Richard Smith & Robert Taylor, .
"Additional Critical Values and Asymptotic Representations for Seasonal Unit Root Tests,"
95/43, Department of Economics, University of York.
- Smith, Richard J. & Taylor, A. M. Robert, 1998. "Additional critical values and asymptotic representations for seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 85(2), pages 269-288, August.
- Smith, R.J. & Taylor, R., 1995. "Additional Critical Values and Asymptotic Representations for Seasonal Unit Roots Tests," Cambridge Working Papers in Economics 9529, Faculty of Economics, University of Cambridge.
- Ghysels,Eric & Osborn,Denise R., 2001.
"The Econometric Analysis of Seasonal Time Series,"
Cambridge University Press, number 9780521565882, 1.
- 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.
- Osborn, Denise R., 1993. "Seasonal cointegration," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 299-303.
- Rodrigues, Paulo M. M. & Taylor, A. M. Robert, 2004. "Alternative estimators and unit root tests for seasonal autoregressive processes," Journal of Econometrics, Elsevier, vol. 120(1), pages 35-73, May.
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