Inference of Seasonal Cointegration : Gaussian Reduced Rank Estimation and Tests for Various Types of Cointegration

An extension of Gaussian reduced rank estimation of Ahn and Reinsel (Journal of Econometrics, Vol. 62, pp. 317-350, 1994) to seasonal periods other than four is presented. Simple adjustments for estimation that are necessary because of complex-valued seasonal unit roots are presented in detail and the asymptotic distribution of the estimators that takes the same form as that in Ahn and Reinsel (1994) is derived. Tests for contemporaneous cointegration and common polynomial cointegrating vectors (PCIVs) for different seasonal unit roots are presented. Finite sample properties are briefly examined through a small Monte Carlo simulation study and a numerical example is presented to illustrate the methods