GMM Estimation for Seasonal Cointegration

Park, Suk-Kyung;Cho, Sin-Sup;Seon, Byeong-Chan

  • Received : 20101100
  • Accepted : 20110200
  • Published : 2011.04.30


This paper considers a generalized method of moments(GMM) estimation for seasonal cointegration as the extension of Kleibergen (1999). We propose two iterative methods for the estimation according to whether parameters in the model are simultaneously estimated or not. It is shown that the GMM estimator coincides in form to a maximum likelihood estimator or a feasible two-step estimator. In addition, we derive its asymptotic distribution that takes the same form as that in Ahn and Reinsel (1994).


Generalized method of moments estimation;vector error correction model;vector autoregressive model


  1. Ahn, S. K., Cho, S. and Seong, B. C. (2004). Inference of seasonal cointegration: Gaussian reduced rank estimation and tests for various types of cointegration, Oxford Bulletin of Economics and Statistics, 66, 261–284.
  2. Ahn, S. K. and Reinsel, G. C. (1994). Estimation of partially nonstationary vector autoregressive models with seasonal behavior, Journal of Econometrics, 62, 317–350.
  3. Bruggemann, R. and L¨utkepohl, H. (2005). Practical problems with reduced-rank ML estimators for cointegration parameters and a simple alternative, Oxford Bulletin of Economics and Statistics, 67, 673–690.
  4. Cubadda, G. (2001). Complex reduced rank models for seasonally cointegrated time series, Oxford Bulletin of Economics and Statistics, 63, 497–511.
  5. Engle, R. F. and Granger, C. W. J. (1987). Cointegration and error correction: Representation, estimation and testing, Econometrica, 55, 251–276.
  6. Gonzalo, J. (1994). Five alternative methods of estimating long-run equilibrium relationships, Journal of Econometrics, 60, 203–233.
  7. Hansen, G., Kim, J. R. and Mittnik, S. (1998). Testing cointegrating coefficients in vector autoregressive error correction models, Economics Letters, 58, 1–5.
  8. Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators, Econometrica, 50, 1029–1054.
  9. Hylleberg, S., Engle, R. F., Granger, C. W. J. and Yoo, B. S. (1990). Seasonal integration and cointegration, Journal of Econometrics, 44, 215–238.
  10. Johansen, S. and Schaumburg, E. (1999). Likelihood analysis of seasonal cointegration, Journal of Econometrics, 88, 301–339.
  11. Kitamura, Y. and Phillips, P. C. B. (1997). Fully modified IV, GIVE and GMM estimation with possibly nonstationary regressors and instruments, Journal of Econometrics, 80, 85–123.
  12. Kleibergen, F. (1999). Reduced Rank Regression Using Generalized Method of Moments Estimators, In L. Matyas (Ed), Generalized method of moments estimation, Cambridge University Press, Cambridge.
  13. Phillips, P. C. B. (1994). Some exact distribution theory for maximum likelihood estimators of cointegrating coefficients in error correction models, Econometrica, 62, 73–93.
  14. Quintos, C. E. (1998). Analysis of cointegration vectors using the GMM approach, Journal of Econometrics, 85, 155–188.
  15. Seong, B. (2008). A feasible two-step estimator for seasonal cointegration, Communications of the Korean Statistical Society, 15, 411–420.