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The behaviour of the likelihood function for ARMA models

Published online by Cambridge University Press:  01 July 2016

M. Deistler  and
B. M. Pötscher
M. Deistler*
Affiliation:
University of Technology, Vienna
B. M. Pötscher*
Affiliation:
University of Technology, Vienna
*
∗ Postal address: Institute of Econometrics and Operations Research, University of Technology, A-1040 Vienna, Argentinierstr. 8, Austria.
∗ Postal address: Institute of Econometrics and Operations Research, University of Technology, A-1040 Vienna, Argentinierstr. 8, Austria.
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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

EXISTENCE OF A MAXIMUMMAXIMUM LIKELIHOOD ESTIMATION

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 4 , December 1984 , pp. 843 - 866
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

Support by ‘Fonds zur Förderung der wissenschaftlichen Forschung', project No. 4393, is gratefully acknowledged.

References

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