Inference of Seasonal Cointegration: Gaussian Reduced Rank Estimation and Tests for Various Types of Cointegration*
将高斯降秩估计法推广到任意季节周期，详细处理了复值季节性单位根带来的估计调整，推导了与Ahn和Reinsel（1994）形式相同的渐近分布，并提出了同期协整和公共多项式协整向量的检验，通过蒙特卡洛模拟和数值例子验证了有限样本性质。
Abstract 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.