Semiparametric error-correction models for cointegration with trends: Pseudo-Gaussian and optimal rank-based tests of the cointegration rank

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This paper provides pseudo-Gaussian and locally optimal rank-based tests for the cointegration rank in linear cointegrated error-correction models with common trends and 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.
Original languageEnglish
Pages (from-to)46-61
Number of pages15
JournalJournal of Econometrics
Issue number1
Publication statusPublished - 1 Jan 2016



  • Cointegration model
  • Cointegration rank
  • Elliptical densities
  • Error-correction model
  • Lagrange multiplier test
  • Local asymptotic Brownian functional
  • Local asymptotic mixed normality
  • Local asymptotic normality
  • Multivariate ranks
  • Quasi-likelihood procedures
  • Rank tests
  • Semiparametric efficiency

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