Bootstrap Testing of Hypotheses on Co-Integration Relations in Vector Autoregressive Models
针对向量自回归模型中协整向量假设检验有限样本性质差的问题，提出一种在Bootstrap样本中施加原假设的新检验方法，证明其渐近有效且优于现有方法。
It is well known that the finite-sample properties of tests of hypotheses on the cointegrating vectors in vector autoregressive models can be quite poor, and that current solutions based on Bartlett-type corrections or bootstrap based on unrestricted parameter estimators are unsatisfactory, in particular in those cases where also asymptotic chi^2 tests fail most severely. In this paper, we solve this inference problem by showing \nthe novel result that a bootstrap test where the null hypothesis is imposed on the bootstrap sample is asymptotically valid. That is, not only does it have asymptotically correct size, but, in contrast to what is claimed in existing literature, it is consistent under the alternative. Compared to the theory for bootstrap tests on the co-integration rank \n(Cavaliere, Rahbek, and Taylor (2012)), establishing the validity of the bootstrap in the framework of hypotheses on the co-integrating vectors requires new theoretical developments, including the introduction of multivariate Ornstein–Uhlenbeck processes with random (reduced rank) drift parameters. Finally, as documented by Monte Carlo simulations, the bootstrap test outperforms existing methods.