Authors: Hallin, Marc
van den Akker, Ramon
Werker, Bas J. M.
Title: Rank-based tests of the cointegrating rank in semiparametric error correction models
Language (ISO): en
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.
Subject Headings: 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
Issue Date: 2012-12-04
Appears in Collections:Sonderforschungsbereich (SFB) 823

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