Minimum Phase Estimation

  • Murray Rosenblatt
Part of the Springer Series in Statistics book series (SSS)

Abstract

We shall in this section consider the asymptotic behavior of parameter estimates in the case of one-dimensional minimum phase ARMA schemes that are equivalent asymptotically in the Gaussian case to maximum likelihood estimates. Consider the stationary ARMA (p, q) minimum phase sequence {xt}
$$ {x_{t}} - {\phi _{1}}{x_{t}}_{{ - 1}} - \cdots - {\phi _{p}}{x_{{t - p}}} = {\xi _{t}} + {\theta _{1}}{\xi _{{t - 1}}} + \cdots + {\theta _{q}}{\xi _{{t - q}}} $$
(2.1.1)
with the ξ t ’s independent, identically distributed with mean zero and variance σ2.

Keywords

Covariance 

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Murray Rosenblatt
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaSan Diego La JollaUSA

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