Bootstrap Cointegration Rank Testing: The Role of Deterministic Variables and Initial Values in the Bootstrap Recursion
研究了自举递归中是否包含估计的确定性成分和非零初始值对协整秩检验的影响，发现对OLS去趋势检验，更简单的做法（不包含确定性成分、初始值设为零）更优；对GLS去趋势检验，Trenkler（2009）的方法能改善有限样本表现。
In this paper we investigate the role of deterministic components and initial values in bootstrap likelihood ratio type tests of cointegration rank. A number of bootstrap procedures have been proposed in the recent literature some of which include estimated deterministic components and nonzero initial values in the bootstrap recursion while others do the opposite. To date, however, there has not been a study into the relative performance of these two alternative approaches. In this paper we fill this gap in the literature and consider the impact of these choices on both ordinary least squares (OLS) and generalized least squares (GLS) detrended tests, in the case of the latter proposing a new bootstrap algorithm as part of our analysis. Overall, for OLS detrended tests our findings suggest that it is preferable to take the computationally simpler approach of not including estimated deterministic components in the bootstrap recursion and setting the initial values of the bootstrap recursion to zero. For GLS detrended tests, we find that the approach of Trenkler (2009 Trenkler , C. ( 2009 ). Bootstrapping systems cointegration tests with a prior adjustment for deterministic terms . Econometric Theory 25 : 243 – 269 .[Crossref], [Web of Science ®] , [Google Scholar]), who includes a restricted estimate of the deterministic component in the bootstrap recursion, can improve finite sample behavior further.