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

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages77
Volume2012-089
Publication statusPublished - 2012

Publication series

NameCentER Discussion Paper
Volume2012-089

Fingerprint

Error Correction Model
Semiparametric Efficiency
Lagrange multiplier Test
Normal Structure
Non-stationary Time Series
Quasi-likelihood
Distribution-free
Local Structure
Linearity
Asymptotic Analysis
Statistics
Alternatives
Approximation
Experiment
Simulation
Innovation
Model

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

Cite this

Hallin, M., van den Akker, R., & Werker, B. J. M. (2012). Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models. (CentER Discussion Paper; Vol. 2012-089). Tilburg: Econometrics.
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title = "Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models",
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.",
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",
author = "M. Hallin and {van den Akker}, R. and B.J.M. Werker",
note = "Pagination: 77",
year = "2012",
language = "English",
volume = "2012-089",
series = "CentER Discussion Paper",
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Hallin, M, van den Akker, R & Werker, BJM 2012 'Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models' CentER Discussion Paper, vol. 2012-089, Econometrics, Tilburg.

Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models. / Hallin, M.; van den Akker, R.; Werker, B.J.M.

Tilburg : Econometrics, 2012. (CentER Discussion Paper; Vol. 2012-089).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models

AU - Hallin, M.

AU - van den Akker, R.

AU - Werker, B.J.M.

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PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

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 - non-Gaussian Quasi-Likelihood Procedures

M3 - Discussion paper

VL - 2012-089

T3 - CentER Discussion Paper

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

PB - Econometrics

CY - Tilburg

ER -