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Asymptotic Likelihood Based Inference for Co-integrated Homogenous Gaussian Diffusions

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In this paper we consider inference for a multivariate Gaussian homogenous diffusion which is co-integrated, i.e. admits a representation in terms of stable relations (ergodic diffusions) plus Brownian motions. We show that inference on co-integration rank (the number of stable relations) in continuous time can be based on existing asymptotic distributions from discrete time co-integration analysis. Likewise the asymptotic distributions of the co-integration parameters are shown to be mixed Gaussian. Special attention is given to the parametrization of the drift terms. It is shown that the asymptotic distribution of the co-integration rank test statistic does not depend on the level of the process as a result of the chosen parametrization.
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Keywords: canonical correlations; co-integration in continuous time; estimation; integrated processes; multidimensional Gaussian diffusion; reduced rank

Document Type: Research Article

Affiliations: 1: Universidad Politecnica de Cartagena 2: University of Copenhagen

Publication date: 01 August 2001

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