Bootstrap Testing Linear Restrictions on Cointegrating Vectors.

We consider a computer-intensive method for inference on cointegrating vectors in maximum likelihood cointegration analysis. Simulation studies show that the size distortion for the asymptotic likelihood ratio test can be considerable for small samples. It is demonstrated that a parametric bootstrap frequently results in a nearly exact alpha-level test. Furthermore, response surface regression is used to examine small-sample properties of the asymptotic test. In particular, using an extensive experimental design, in which the data-generating processes are based on empirical models, we describe how the complexity of the model affects the degree of size distortion for given sample size.