FULLY MODIFIED ESTIMATION OF SEASONALLY COINTEGRATED PROCESSES
将完全修正最小二乘估计方法扩展到季节协整过程，提出一个检验季节协整存在性的统计量，并通过蒙特卡洛模拟考察其有限样本性质。
We extend the framework of the fully modified, ordinary least squares (OLS) estimator introduced by Phillips and Hansen (1990) to the case of seasonally cointegrated processes at a given frequency. First we extend a weak convergence result of sample covariance matrices (Phillips, 1988) to the case of seasonal unit roots. Using a complex number framework, we then show that we can take into account the constraints that exist in a situation of seasonal cointegration as illustrated in Gregoir (1999a) and derive estimates of the cointegration vectors that allow for asymptotic normal inference. This allows us to propose a test whose null hypothesis is the existence of seasonal cointegration. A Monte Carlo exercise investigates the finite sample properties of this test procedure. The paper closes with the analysis of situations in which there exist more than one frequency at which seasonal cointegration can be observed.