Scandinavian Journal of Statistics

Asymptotic Likelihood Based Inference for Co‐integrated Homogenous Gaussian Diffusions

Journal Article

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.

Related Topics

Related Publications

Related Content

Site Footer


This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.