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A class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests

Author

Listed:
  • Marc Hallin
  • Ramon van den Akker
  • Bas Werker

Abstract

We propose a class of simple rank-based tests for the null hypothesis of a unit root. This class is indexed by the choice of a reference density g, which needs not coincide with the unknown actual innovation density f. The validity of these tests, in terms of exact finite sample size, is guaranteed by distribution-freeness, irrespective of the value of the drift and the actual underlying f. When based on a Gaussian reference density g, our tests (of the van der Waerden form) perform uniformly better, in terms of asymptotic relative effciency, than the Dickey and Fuller test --except under Gaussian f, where they are doing equally well. Under Student t3 density f, the effciency gain is as high as 110%, meaning that Dickey-Fuller requires over twice as many observations as we do in order to achieve comparable performance. This gain is even larger in case the underlying f has fatter tails; under Cauchy f, where Dickey and Fuller is no longer valid, it can be considered infinite. The test associated with reference density g is semiparametrically e±cient when f happens to coincide with g, in the ubiquitous case that the model contains a non-zero drift. Finally, with an estimated density f(n) substituted for the reference density g, our tests achieve uniform (with respect to f) semiparametric efficiency.

Suggested Citation

  • Marc Hallin & Ramon van den Akker & Bas Werker, 2009. "A class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests," Working Papers ECARES 2009_001, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2009_001
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Marc Hallin & Ramon van den Akker & Bas Werker, 2012. "Rank-Based Tests of the Cointegrating Rank in Semiparametric Error Correction Models," Working Papers ECARES ECARES 2012-042, ULB -- Universite Libre de Bruxelles.
    2. 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," Discussion Paper 2015-001, Tilburg University, Center for Economic Research.

    More about this item

    Keywords

    Dickey-Fuller test; Local Asymptotic Normality;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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