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Non-Gaussian Estimation

  • György Terdik
Part of the Lecture Notes in Statistics book series (LNS, volume 142)

Abstract

Recently, considerable attention has been paid to nonlinear models in time series analysis. The fact is, most of the time series in practice are not Gaussian, and the second order statistics of a bilinear model, for example, does not contain any information about the parameters of nonlinearity, see Terdik and Subba Rao [139]. The methods of parameter estimation are usually based on either the covariances as Yule-Walker equations or the spectrum, see the monographs by Brockwell and Davis [29], Priestley [100], Rosenblatt [107]. These are called Gaussian estimates because they make use of the second order information only. Brillinger [21] started to apply a criterion involving a third order spectrum, i.e., a bispectrum as well as a second order one and found improvement in estimates. The idea is that the theoretical and the estimated spectra are compared by an iteratively reweighted least squares procedure. The idea of Gaussian estimation in the second order case goes back essentially to the method suggested by Whittle [144]. The properties of such types of estimates are studied by Rice [106], using the asymptotic properties of the spectral estimators due to Brillinger and Rosenblatt [27], and discussed by several authors such as Walker [142], [143], [35] and Hannan [50]. The handicap of the nonGaussian parameter estimation is that the exact spectral and bispectral densities are supposed to be known up to some parameters of the model. The models that have been successfully considered are the linear (nonGaussian) Brillinger [21] and the bilinear one Terdik [131].

Keywords

Asymptotic Variance Linear Process Bilinear Model Spectral Estimator Fourier Frequency 
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 1999

Authors and Affiliations

  • György Terdik
    • 1
  1. 1.Center for Informatics and ComputingKossuth University of DebrecenDebrecen 4010Hungary

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