Inference of seasonal cointegration with linear restrictions

Abstract

In this article, we study the statistical inference of seasonal cointegration with joint linear restrictions among cointegrating vectors associated with possibly different seasonal unit roots. A Wald-type test and a likelihood ratio test are considered. For the development of the test statistics, we use the Gaussian reduced-rank estimation of Ahn et al. [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], which simultaneously accommodates the cointegration corresponding to all seasonal unit roots. We then obtain the asymptotic distributions of the test statistics. We present methods for accommodating linear restrictions in the Gaussian reduced-rank estimation and obtain the related asymptotic distributions. A Monte Carlo simulation is conducted to investigate small-sample properties of the test statistics for some linear restrictions.

Keywords:

• Hypothesis testing
• Cointegrating vectors
• Gaussian reduced-rank estimation
• Seasonal unit root

Acknowledgements

The authors thank an anonymous referee for the helpful comments that led to a significant improvement of this article. Byeongchan Seong was supported by the Post-doctoral Fellowship Program of Korea Science and Engineering Foundation (KOSEF). The research of Sinsup Cho and Sung K. Ahn was supported by the Korea Research Foundation Grant (KRF-2005-070-C00022) funded by the Korean Government (MOEHRD).