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Rank-Based Tests of the Cointegrating Rank in Semiparametric Error Correction Models

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  • Marc Hallin
  • Ramon van den Akker
  • Bas Werker

Abstract

This paper introduces rank-based tests for the cointegrating rank in an Error CorrectionModel with i.i.d. elliptical innovations. The tests are asymptotically distribution-free,and their validity does not depend on the actual distribution of the innovations. Thisresult holds despite the fact that, depending on the alternatives considered, the model exhibitsa non-standard Locally Asymptotically Brownian Functional (LABF) and LocallyAsymptotically Mixed Normal (LAMN) local structure—a structure which we completelycharacterize. Our tests, which have the general form of Lagrange multiplier tests, dependon a reference density that can freely be chosen, and thus is not restricted to be Gaussianas in traditional quasi-likelihood procedures. Moreover, appropriate choices of the referencedensity are achieving the semiparametric efficiency bounds. Simulations show thatour asymptotic analysis provides an accurate approximation to finite-sample behavior.Our results are based on an extension, of independent interest, of two abstract resultson the convergence of statistical experiments and the asymptotic linearity of statistics tothe context of, possibly non-stationary, time series

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Bibliographic Info

Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number ECARES 2012-042.

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Length: 76 p.
Date of creation: Nov 2012
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Publication status: Published by:
Handle: RePEc:eca:wpaper:2013/132503

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Keywords: 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; non-Gaussian Quasi-Likelihood Procedures;

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References

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