The asymptotic CRLB for the spectrum of ARMA processes
Ninness, B.
Sch. of Electr. Eng. & Comput. Sci., Univ. of Newcastle, Callaghan, NSW, Australia;
This paper appears in: Signal Processing, IEEE Transactions on
Publication Date: June 2003
Volume: 51,
Issue: 6
On page(s): 1520- 1531
ISSN: 1053-587X
INSPEC Accession Number: 7684129
Digital Object Identifier: 10.1109/TSP.2003.811244
Current Version Published: 2003-05-21
Abstract
This paper addresses the issue of quantifying the frequency domain accuracy of autoregressive moving average (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 that, for AR models, are exact for finite model order. By employing new analysis methods based on rational orthonormal parameterizations, 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.
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