Asymptotic Likelihood Based Inference for Co-integrated Homogenous Gaussian Diffusions
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.
No Supplementary Data
No Article Media