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

Fingerprint

Cointegration
Error correction model
Innovation
Semiparametric efficiency bound
Asymptotic analysis
Approximation
Finite sample
Simulation
Distribution-free
Cointegration test

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.
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title = "Optimal Pseudo-Gaussian and Rank-based Tests of the Cointegration Rank in Semiparametric Error-correction Models",
abstract = "This paper provides locally optimal pseudo-Gaussian and rank-based tests forthe 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, associatedwith 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-Gaussiancounterparts. 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.",
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",
author = "M. Hallin and B.J.M. Werker and {van den Akker}, R.",
year = "2015",
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language = "English",
volume = "2015-001",
series = "CentER Discussion Paper",
publisher = "CentER, Center for Economic Research",
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Hallin, M, Werker, BJM & 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, CentER, Center for Economic Research, Tilburg.

Optimal Pseudo-Gaussian and Rank-based Tests of the Cointegration Rank in Semiparametric Error-correction Models. / Hallin, M.; Werker, B.J.M.; van den Akker, R.

Tilburg : CentER, Center for Economic Research, 2015. (CentER Discussion Paper; Vol. 2015-001).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Optimal Pseudo-Gaussian and Rank-based Tests of the Cointegration Rank in Semiparametric Error-correction Models

AU - Hallin, M.

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N2 - This paper provides locally optimal pseudo-Gaussian and rank-based tests forthe 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, associatedwith 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-Gaussiancounterparts. 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.

AB - This paper provides locally optimal pseudo-Gaussian and rank-based tests forthe 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, associatedwith 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-Gaussiancounterparts. 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.

KW - Cointegration model

KW - Cointegration rank

KW - Elliptical densities

KW - erro-correction model

KW - Lagrange multiplier test

KW - Local Asymptotic Brownian Functional

KW - Local Asymptotic Mixed Normality

KW - Local Asymptotic Normality

KW - Multivariate ranks

KW - quasi-likelihood procedures

M3 - Discussion paper

VL - 2015-001

T3 - CentER Discussion Paper

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

PB - CentER, Center for Economic Research

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Hallin M, Werker BJM, van den Akker R. Optimal Pseudo-Gaussian and Rank-based Tests of the Cointegration Rank in Semiparametric Error-correction Models. Tilburg: CentER, Center for Economic Research. 2015 Jan 8. (CentER Discussion Paper).