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

Marc Hallin (), R. van den Akker and Bas Werker ()
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R. van den Akker: Tilburg University, Center For Economic Research

No 2012-089, Discussion Paper from Tilburg University, Center for Economic Research

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 (search for similar items in EconPapers)
JEL-codes: C14 C32 (search for similar items in EconPapers)
Date: 2012
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