On Spectral Analysis Using Models with Pre-specified Zeros

Abstract

The fundamental theory of Lindquist and co-workers on the rational covariance extension problem provides a very elegant framework for ARMA spectral estimation. Here the choice of zeros is completely arbitrary, and can be used to tune the estimator. An alternative approach to ARMA model estimation with pre-specified zeros is to use a prediction error method based on generalizing autoregressive (AR) modeling using orthogonal rational filters. Here the motivation is to reduce the number of parameters needed to obtain useful approximate models of stochastic processes by suitable choice of zeros, without increasing the computational complexity.

The objective of this contribution is to discuss similarities and differences between these two approaches to spectral estimation.