Rank-Based Tests of the Cointegrating Rank in Semiparametric Error Correction Models
Copyright policy )Rank-Based Tests of the Cointegrating Rank in Semiparametric Error Correction Models
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.
Discussion Paper / SFB 823;56/2012
- TU Dortmund University Germany
- Tilburg University Netherlands
- Université Libre de Bruxelles
- Université Libre de Bruxelles Belgium
- Université Libre de Bruxelles
330, Semiparametric and Nonparametric Methods, 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, error correction model, Multiple or Simultaneous Equation Models: Time-Series Models, Time-Series Models [Multiple or Simultaneous Equation Models], 310, Local Asymptotic Normality, Local asymptotic Mixed Normality, 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, Multivariate ranks, Local Asymptotic Mixed Normality, C14, Cointegration model, Elliptical densities, info:eu-repo/classification/ddc/310, C32, non-Gaussian Quasi-Likelihood Procedures, info:eu-repo/classification/ddc/330, Error correction model, Lagrange Multiplier test, Multivariate Ranks, local asymptotic Brownian Functional, Cointegration rank, Local Asymptotic Brownian Functional, 620, 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, Local asymptotic Normality, Economie, info:eu-repo/classification/ddc/620, Cointegration Rank, Lagrange multiplier test, jel: jel:C32, jel: jel:C14
330, Semiparametric and Nonparametric Methods, 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, error correction model, Multiple or Simultaneous Equation Models: Time-Series Models, Time-Series Models [Multiple or Simultaneous Equation Models], 310, Local Asymptotic Normality, Local asymptotic Mixed Normality, 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, Multivariate ranks, Local Asymptotic Mixed Normality, C14, Cointegration model, Elliptical densities, info:eu-repo/classification/ddc/310, C32, non-Gaussian Quasi-Likelihood Procedures, info:eu-repo/classification/ddc/330, Error correction model, Lagrange Multiplier test, Multivariate Ranks, local asymptotic Brownian Functional, Cointegration rank, Local Asymptotic Brownian Functional, 620, 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, Local asymptotic Normality, Economie, info:eu-repo/classification/ddc/620, Cointegration Rank, Lagrange multiplier test, jel: jel:C32, jel: jel:C14
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