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Numerical Distribution Functions for Seasonal Unit Root Tests

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  • Díaz-Emparanza Herrero, Ignacio

Abstract

When working with time series data observed at intervals smaller than a year, it is often necessary to test for the presence of seasonal unit roots. One of the most widely used methods for testing seasonal unit roots is that of HEGY, which provides test statistics with non-standard distributions. This paper describes a generalisation of this method for any periodicity and uses a response surface regressions approach to calculate the critical values and P values of the HEGY statistics whatever the periodicity and sample size of the data. The algorithms are prepared with the Gretl open source econometrics package and some new tables of critical values for daily, hourly and half-hourly data are presented.

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Paper provided by Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística) in its series BILTOKI with number 2011-09.

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Date of creation: Dec 2011
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Handle: RePEc:ehu:biltok:5568

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Keywords: seasonality; unit roots; surface response analysis;

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  1. MacKinnon, James G, 1996. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 601-18, Nov.-Dec..
  2. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  3. James G. MacKinnon, 1992. "Approximate Asymptotic Distribution Functions for Unit Roots and Cointegration Tests," Working Papers 861, Queen's University, Department of Economics.
  4. 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.
  5. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  6. George Marsaglia & Wai Wan Tsang, . "The Ziggurat Method for Generating Random Variables," Journal of Statistical Software, American Statistical Association, vol. 5(i08).
  7. 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.
  8. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
  9. 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.
  10. Serena Ng & Pierre Perron, 2001. "A Note on the Selection of Time Series Models," Boston College Working Papers in Economics 500, Boston College Department of Economics.
  11. John Conlisk, 1974. "Optimal Response Surface Design in Monte Carlo Sampling Experiments," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 3, pages 17-28 National Bureau of Economic Research, Inc.
  12. Osborn, Denise R, et al, 1988. "Seasonality and the Order of Integration for Consumption," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 50(4), pages 361-77, November.
  13. Giovanni Baiocchi, 2007. "Reproducible research in computational economics: guidelines, integrated approaches, and open source software," Computational Economics, Society for Computational Economics, vol. 30(1), pages 19-40, August.
  14. Harvey, David I. & van Dijk, Dick, 2006. "Sample size, lag order and critical values of seasonal unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2734-2751, June.
  15. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  16. Hertel, Ida & Kohler, Michael, 2013. "Estimation of the optimal design of a nonlinear parametric regression problem via Monte Carlo experiments," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 1-12.
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Cited by:
  1. Díaz-Emparanza Herrero, Ignacio & Moral Zuazo, María Paz, . "Seasonal Stability Tests in gretl. An Application to International Tourism Data," BILTOKI BILTOKI;2013-03, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).

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