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

Author

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  • Hallin, M.
  • van den Akker, R.

    (Tilburg University, Center For Economic Research)

  • Werker, B.J.M.

    (Tilburg University, Center For Economic Research)

Abstract

Abstract: This paper introduces rank-based tests for the cointegrating rank in an Error Correction Model 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. This result holds despite the fact that, depending on the alternatives considered, the model exhibits a non-standard Locally Asymptotically Brownian Functional (LABF) and Locally Asymptotically Mixed Normal (LAMN) local structure—a structure which we completely characterize. Our tests, which have the general form of Lagrange multiplier tests, depend on a reference density that can freely be chosen, and thus is not restricted to be Gaussian as in traditional quasi-likelihood procedures. Moreover, appropriate choices of the reference density are achieving the semiparametric efficiency bounds. Simulations show that our asymptotic analysis provides an accurate approximation to finite-sample behavior. Our results are based on an extension, of independent interest, of two abstract results on the convergence of statistical experiments and the asymptotic linearity of statistics to the context of, possibly non-stationary, time series.

Suggested Citation

  • Hallin, M. & van den Akker, R. & Werker, B.J.M., 2012. "Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models," Discussion Paper 2012-089, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:bc68a2f2-3ca3-443c-b3ac-f8ef56841037
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    References listed on IDEAS

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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;

    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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