Published online by Cambridge University Press: 01 July 2016
The paper deals with some properties of the (Gaussian) likelihood function for multivariable ARMA models. Its behaviour at the boundary of the parameter space is described; its continuity properties as well as the question of the existence of a maximum are discussed. We have not been able to show in general the existence of the maximum over the usual parameter spaces. However, the maximum always exists over a suitably enlarged parameter space (given that the data are non-degenerate), which includes parameters corresponding to processes with discrete spectral components.
Support by ‘Fonds zur Förderung der wissenschaftlichen Forschung', project No. 4393, is gratefully acknowledged.