- Title
- The asymptotic CRLB for the spectrum of ARMA processes
- Creator
- Ninness, Brett
- Relation
- IEEE Transactions on Signal Processing Vol. 51, Issue 6, p. 1520-1531
- Publisher Link
- http://dx.doi.org/10.1109/TSP.2003.811244
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- journal article
- Date
- 2003
- Description
- This paper addresses the issue of quantifying the frequency domain accuracy of ARMA spectral estimates as dictated by the Cramer--Rao Lower Bound (CRLB). Classical work in this area has led to expressions that are asymptotically exact as both data length and model order tend to infinity, although they are commonly used in finite model order and finite data length settings as approximations. More recent work has established quantifications which, for AR models, are exact for finite model order. By employing new analysis methods based on rational orthonormal parameterisations, together with the ideas of reproducing kernel Hilbert spaces, this paper develops quantifications that extend this previous work by being exact for finite model order in all of the AR, MA and ARMA system cases. These quantifications, via their explicit dependence on poles and zeros of the underlying spectral factor, reveal certain fundamental aspects of the accuracy achievable by spectral estimates of ARMA processes.
- Subject
- ARMA modeling; Crámer-Rao bound; maximum likelihood estimation; spectrum estimation
- Identifier
- http://hdl.handle.net/1959.13/30297
- Identifier
- uon:2671
- Identifier
- ISSN:1053-587X
- Rights
- Copyright © 2006 IEEE. Reprinted from IEEE Transactions on Signal Processing, Vol. 51, Issue 6, p. 1520-1531. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Newcastle's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
- Language
- eng
- Full Text
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