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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

Maximum Likelihood Estimate Asymptotic Distribution Asymptotic Normality Minimum Phase Lower Semicontinuous Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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