Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Estimation of Seasonal Cointegration under Conditional Heteroskedasticity

  • Received : 2015.07.26
  • Accepted : 2015.10.12
  • Published : 2015.11.30
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Abstract

We consider the estimation of seasonal cointegration in the presence of conditional heteroskedasticity (CH) using a feasible generalized least squares method. We capture cointegrating relationships and time-varying volatility for long-run and short-run dynamics in the same model. This procedure can be easily implemented using common methods such as ordinary least squares and generalized least squares. The maximum likelihood (ML) estimation method is computationally difficult and may not be feasible for larger models. The simulation results indicate that the proposed method is superior to the ML method when CH exists. In order to illustrate the proposed method, an empirical example is presented to model a seasonally cointegrated times series under CH.

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References

  1. Ahn, S. K. and Reinsel, G. C. (1994). Estimation of partially nonstationary vector autoregressive models with seasonal behavior, Journal of Econometrics, 62, 317-350. https://doi.org/10.1016/0304-4076(94)90027-2
  2. 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. https://doi.org/10.1111/j.0305-9049.2003.00100.x
  3. Berndt, E. K., Hall, B. H., Hall, R. E. and Hausman, J. A. (1974). Estimation and inference in nonlinear structural models, Annals of Economic and Social Measurement, 3/4, 653-665.
  4. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  5. Engle, R. F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models, Journal of Business & Economic Statistics, 20, 339-350. https://doi.org/10.1198/073500102288618487
  6. Engle, R. F. and Granger, C. W. (1987). Co-integration and error correction: Representation, estimation, and testing, Econometrica, 55, 251-276. https://doi.org/10.2307/1913236
  7. Engle, R. F. and Kroner, K. F. (1995). Multivariate simultaneous generalized ARCH, Econometric Theory, 11, 122-150. https://doi.org/10.1017/S0266466600009063
  8. Herwartz, H. and Lutkepohl, H. (2011). Generalized least squares estimation for cointegration parameters under conditional heteroskedasticity, Journal of Time Series Analysis, 32, 281-291. https://doi.org/10.1111/j.1467-9892.2010.00698.x
  9. Johansen, S. (1988). Statistical analysis of cointegration vectors, Journal of Economic Dynamics and Control, 12, 231-254. https://doi.org/10.1016/0165-1889(88)90041-3
  10. Lutkepohl, H. (2005). New Introduction to Multiple Time Series Analysis, Springer-Verlag, Berlin.
  11. Seo, B. (2007). Asymptotic distribution of the cointegrating vector estimator in error correction models with conditional heteroskedasticity, Journal of Econometrics, 137, 68-111. https://doi.org/10.1016/j.jeconom.2006.03.008
  12. Seong, B. (2013). Semiparametric selection of seasonal cointegrating ranks using information criteria, Economics Letters, 120, 592-595. https://doi.org/10.1016/j.econlet.2013.06.031
  13. Seong, B., Cho, S. and Ahn, S.K. (2006). Maximum eigenvalue test for seasonal cointegrating ranks, Oxford Bulletin of Economics and Statistics, 68, 497-514. https://doi.org/10.1111/j.1468-0084.2006.00174.x
  14. van derWeide, R. (2002). GO-GARCH: A multivariate generalized orthogonal GARCH model, Journal of Applied Econometrics, 17, 549-564. https://doi.org/10.1002/jae.688