Semiparametric error-correction models for cointegration with trends

Pseudo-Gaussian and optimal rank-based tests of the cointegration rank

Research output: Contribution to journalArticleScientificpeer-review

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.
Original languageEnglish
Pages (from-to)46-61
Number of pages15
JournalJournal of Econometrics
Volume190
Issue number1
DOIs
Publication statusPublished - 1 Jan 2016

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

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

Cite this

@article{5e5fdf92261d419280d3e812f90b50f6,
title = "Semiparametric error-correction models for cointegration with trends: Pseudo-Gaussian and optimal rank-based tests of the cointegration rank",
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.",
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",
author = "M. Hallin and {van den Akker}, Ramon and Bas Werker",
year = "2016",
month = "1",
day = "1",
doi = "10.1016/j.jeconom.2015.08.003",
language = "English",
volume = "190",
pages = "46--61",
journal = "Journal of Econometrics",
issn = "0304-4076",
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Semiparametric error-correction models for cointegration with trends : Pseudo-Gaussian and optimal rank-based tests of the cointegration rank. / Hallin, M.; van den Akker, Ramon; Werker, Bas.

In: Journal of Econometrics, Vol. 190, No. 1, 01.01.2016, p. 46-61.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Semiparametric error-correction models for cointegration with trends

T2 - Pseudo-Gaussian and optimal rank-based tests of the cointegration rank

AU - Hallin, M.

AU - van den Akker, Ramon

AU - Werker, Bas

PY - 2016/1/1

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N2 - 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.

AB - 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.

KW - Cointegration model

KW - Cointegration rank

KW - Elliptical densities

KW - Error-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

KW - Rank tests

KW - Semiparametric efficiency

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JF - Journal of Econometrics

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