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Tests of seasonal integration and cointegration in multivariate unobserved component models

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  • Fabio Busetti

    (Bank of Italy, Research Department, Via Nazionale 91, 00184 Rome, Italy)

Abstract

This paper considers tests of seasonal integration and cointegration for multivariate unobserved component models. First, 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. Then the null hypothesis of seasonal cointegration is considered and a test for common nonstationary components at the seasonal frequencies is proposed. 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. Finally, the tests are applied to the series of industrial production of the four largest countries of the European Monetary Union. It is found that Germany does not appear to cointegrate with the other countries at most seasonal frequencies, while there seems to exist a common nonstationary seasonal component between France, Italy and Spain. Copyright © 2006 John Wiley & Sons, Ltd.

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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 21 (2006)
Issue (Month): 4 ()
Pages: 419-438

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Handle: RePEc:jae:japmet:v:21:y:2006:i:4:p:419-438

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  1. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-36, July.
  2. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "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?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
  3. Joseph Beaulieu, J. & Miron, Jeffrey A., 1993. "Seasonal unit roots in aggregate U.S. data," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 305-328.
  4. 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.
  5. Nyblom, Jukka & Harvey, Andrew, 2000. "Tests Of Common Stochastic Trends," Econometric Theory, Cambridge University Press, vol. 16(02), pages 176-199, April.
  6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  7. Fabio Busetti, 2004. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Econometrics 0411003, EconWPA.
  8. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. Reimers, Hans-Eggert, 1997. "Seasonal Cointegration Analysis of German Consumption Function," Empirical Economics, Springer, vol. 22(2), pages 205-31.
  14. 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.
  15. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, October.
  16. Cubadda, Gianluca & Omtzigt, Pieter, 2005. "Small-sample improvements in the statistical analysis of seasonally cointegrated systems," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 333-348, April.
  17. Harvey, Andrew, 2001. "Testing in Unobserved Components Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(1), pages 1-19, January.
  18. 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.
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Cited by:
  1. Fabio Busetti, 2006. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 419-438.
  2. 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.
  3. El Montasser, Ghassen & Boufateh, Talel & Issaoui, Fakhri, 2013. "The seasonal KPSS test when neglecting seasonal dummies: a Monte Carlo analysis," MPRA Paper 46226, University Library of Munich, Germany.

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