The behaviour of the likelihood function for ARMA models
- 1 December 1984
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 16 (4) , 843-866
- https://doi.org/10.2307/1427343
Abstract
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.Keywords
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