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Tests of seasonal integration and cointegration in multivariate unobserved component models

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  • Fabio Busetti

    (Banca d'Italia)

Abstract

The paper considers tests of seasonal integration and cointegration for multivariate time series. The locally best invariant (LBI) test of the null hypothesis of a deterministic seasonal pattern against the alternative of seasonal integration is derived for a model with Gaussian i.i.d. disturbances and deterministic trend. A test of seasonal cointegration is then proposed, which parallels the common trend test of Nyblom and Harvey (2000). The tests are subsequently generalized to account for stochastic trends, weakly dependent errors and unattended unit roots. Asymptotic representations and critical values of the tests are provided, while the finite sample performance is evaluated by Monte Carlo simulation experiments. We apply the tests to the indices of industrial production of the four largest countries of the European Monetary Union. We find evidence that Germany does not cointegrate with the other countries, while there seems to exist a common nonstationary seasonal component between France, Italy and Spain.

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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0411003.

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Length: 35 pages
Date of creation: 05 Nov 2004
Date of revision:
Handle: RePEc:wpa:wuwpem:0411003

Note: Type of Document - pdf; pages: 35
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Web page: http://128.118.178.162

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Keywords: Common components; Locally best invariant test; Seasonal unit roots;

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References

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  1. Cubadda, Gianluca, 1999. "Common Cycles in Seasonal Non-stationary Time Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 273-91, May-June.
  2. Nyblom, Jukka & Harvey, Andrew, 1999. "Tests of Common Stochastic Trends," Cambridge Working Papers in Economics 9902, Faculty of Economics, University of Cambridge.
  3. Harvey, Andrew, 2001. "Testing in Unobserved Components Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(1), pages 1-19, January.
  4. Reimers, Hans-Eggert, 1997. "Seasonal Cointegration Analysis of German Consumption Function," Empirical Economics, Springer, vol. 22(2), pages 205-31.
  5. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-36, July.
  6. Cubadda, Gianluca & Omtzigt, Pieter, 2003. "Small Sample Improvements in the Statistical Analysis of Seasonally Cointegrated Systems," Economics & Statistics Discussion Papers esdp03012, University of Molise, Dept. EGSeI.
  7. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  8. Franses, Philip Hans & McAleer, Michael, 1998. " Cointegration Analysis of Seasonal Time Series," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 651-78, December.
  9. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  10. Caner, Mehmet, 1998. "A Locally Optimal Seaosnal Unit-Root Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 349-56, July.
  11. Engle, R. F. & Granger, C. W. J. & Hylleberg, S. & Lee, H. S., 1993. "The Japanese consumption function," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 275-298.
  12. Gregoir, St phane, 1999. "Multivariate Time Series With Various Hidden Unit Roots, Part Ii," Econometric Theory, Cambridge University Press, vol. 15(04), pages 469-518, August.
  13. Fabio Busetti, 2003. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Temi di discussione (Economic working papers) 476, Bank of Italy, Economic Research and International Relations Area.
  14. 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.
  15. Ahn, Sung K. & Reinsel, Gregory C., 1994. "Estimation of partially nonstationary vector autoregressive models with seasonal behavior," Journal of Econometrics, Elsevier, vol. 62(2), pages 317-350, June.
  16. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  17. Huang, Tai-Hsin & Shen, Chung-Hua, 2002. "Seasonal cointegration and cross-equation restrictions on a forward-looking buffer stock model of money demand," Journal of Econometrics, Elsevier, vol. 111(1), pages 11-46, November.
  18. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
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Citations

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Cited by:
  1. Fabio Busetti, 2003. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Temi di discussione (Economic working papers) 476, Bank of Italy, Economic Research and International Relations Area.
  2. Ghassen El Montasser & Talel Boufateh & Fakhri Issaoui, 2013. "The Seasonal KPSS Test When Neglecting Seasonal Dummies: A Monte Carlo analysis," EERI Research Paper Series EERI RP 2013/07, Economics and Econometrics Research Institute (EERI), Brussels.
  3. Fabio Busetti & Silvestro di Sanzo, 2011. "Bootstrap LR tests of stationarity, common trends and cointegration," Temi di discussione (Economic working papers) 799, Bank of Italy, Economic Research and International Relations Area.

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