A Comparison of Johansen's, Bierens’ and the Subspace Algorithm Method for Cointegration Analysis*
通过模拟和奥地利增长模型实例，比较三种协整方法在秩检验和空间估计上的表现，发现子空间算法不逊于Johansen法，且两者均优于Bierens法，但结果对变量数和样本量敏感，建议谨慎解读。
Abstract The methods listed in the title are compared by means of a simulation study and a real world application. The aspects compared via simulations are the performance of the tests for the cointegrating rank and the quality of the estimated cointegrating space. The subspace algorithm method, formulated in the state space framework and thus applicable for vector autoregressive moving average (VARMA) processes, performs at least comparably to the Johansen method. Both the Johansen procedure and the subspace algorithm cointegration analysis perform significantly better than Bierens’ method. The real‐world application is an investigation of the long‐run properties of the one‐sector neoclassical growth model for Austria. The results do not fully support the implications of the model with respect to cointegration. Furthermore, the results differ greatly between the different methods. The amount of variability depends strongly upon the number of variables considered and huge differences occur for the full system with six variables. Therefore we conclude that the results of such applications with about five or six variables and 100 observations, which are typical in the applied literature, should possibly be interpreted with more caution than is commonly done.