Rank-based tests of the cointegrating rank in semiparametric error correction models
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Date
2012-12-04
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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.
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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