Optimal Pseudo-Gaussian and Rank-based Tests of the Cointegration Rank in Semiparametric Error-correction Models

This paper provides locally optimal pseudo-Gaussian and rank-based tests for
the cointegration rank in linear cointegrated error-correction models with i.i.d.
elliptical innovations. The proposed tests are asymptotically distribution-free,
hence their validity does not depend on the actual distribution of the innovations.
The proposed rank-based tests depend on the choice of scores, associated
with a reference density that can freely be chosen. Under appropriate choices they are achieving the semiparametric efficiency bounds; when based on Gaussian scores, they moreover uniformly dominate their pseudo-Gaussian
counterparts. Simulations show that the asymptotic analysis provides an accurate approximation to finite-sample behavior. The theoretical results are based on a complete picture of the asymptotic statistical structure of the model under consideration.