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

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  • Hallin, Marc
  • van den Akker, Ramon
  • Werker, Bas J.M.

Abstract

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.

Suggested Citation

  • Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2016. "Semiparametric error-correction models for cointegration with trends: Pseudo-Gaussian and optimal rank-based tests of the cointegration rank," Journal of Econometrics, Elsevier, vol. 190(1), pages 46-61.
    • Handle: RePEc:eee:econom:v:190:y:2016:i:1:p:46-61
    DOI: 10.1016/j.jeconom.2015.08.003
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    More about this item

    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; Quasi-likelihood procedures; Rank tests; Semiparametric efficiency;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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