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

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Abstract

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.
Original languageEnglish
Place of PublicationTilburg
PublisherCentER, Center for Economic Research
Number of pages72
Volume2015-001
Publication statusPublished - 8 Jan 2015

Publication series

NameCentER Discussion Paper
Volume2015-001

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Keywords

  • Cointegration model
  • Cointegration rank
  • Elliptical densities
  • erro-correction model
  • Lagrange multiplier test
  • Local Asymptotic Brownian Functional
  • Local Asymptotic Mixed Normality
  • Local Asymptotic Normality
  • Multivariate ranks
  • quasi-likelihood procedures

Cite this

Hallin, M., Werker, B. J. M., & van den Akker, R. (2015). Optimal Pseudo-Gaussian and Rank-based Tests of the Cointegration Rank in Semiparametric Error-correction Models. (CentER Discussion Paper; Vol. 2015-001). Tilburg: CentER, Center for Economic Research.