Finding Cointegration Rank in High Dimensional Systems Using the Johansen Test: An Illustration Using Data Based Monte Carlo Simulations
用基于真实数据的蒙特卡洛模拟，检验Johansen检验在高维系统中估计单位根个数的能力，发现系统维度和滞后阶数会影响结果，过度参数化与欠参数化同样糟糕，贝叶斯信息准则优于赤池信息准则。
The authors examine the ability of the Johansen (1991) test to estimate the number of unit roots in high dimensional systems. They use data based Monte Carlo methods as a simple means of evaluating the validity of inference using asymptotic critical values. These simulations for a typical annual post-World War II dataset illustrate how the estimated number of unit roots change in a nonmonotone fashion with the dimension of the system, and with the number of lags in the VAR representation. The authors find that overparametrization in high dimensions is as bad as underparametrization. The Bayes information criteria outperforms the Akaike information criteria in their setup. Copyright 1996 by MIT Press.