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Using the HEGY Procedure When Not All Roots Are Present

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Author Info
Tomas del Barrio Castro (Universitat de Barcelona)

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Abstract

Empirical studies have shown little evidence to support the presence of all unit roots present in the filter in quarterly seasonal time series. This paper analyses the performance of the Hylleberg, Engle, Granger and Yoo (1990) (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 4 (1 L),(1+ L), (1+ L2 ), (1 L2 ) and (1+ L + L2 + L3 ) 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 / 2 and two combinations of the previous cases. We show both theoretically and through a Monte-Carlo analysis that the t-ratios and 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 1 t 2 t / 2 .

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Paper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 170.

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Length: 31 pages
Date of creation: 2007
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Handle: RePEc:bar:bedcje:2007170

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Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques. Tinent Coronel Valenzuela, Num 1-11 08034 Barcelona. Spain.
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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing

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  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. [Downloadable!]
  2. 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.
  3. 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. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
  5. Smith, R.J. & Taylor, A.M.R., 1999. "Regression-Based Seasonal Unit Root Tests," Discussion Papers 99-15, Department of Economics, University of Birmingham.
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  6. 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. [Downloadable!] (restricted)
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  7. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-93, January. [Downloadable!] (restricted)
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  8. 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. [Downloadable!] (restricted)
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  9. 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. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Osborn, Denise R., 1993. "Seasonal cointegration," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 299-303. [Downloadable!] (restricted)
  12. 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. [Downloadable!]
  13. Hylleberg, Svend & Jorgensen, Clara & Sorensen, Nils Karl, 1993. "Seasonality in Macroeconomic Time Series," Empirical Economics, Springer, vol. 18(2), pages 321-35.
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