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.