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Abstract

A stationary Gaussian time series has the following properties: (i) the residual series of the moving average representation is a sequence of independent (and Gaussian) series and (ii) the best predictor, i.e., the conditional expectation of the observation according to the past is linear. Both properties lead to the notion of the linearity of a time series. We follow Hannan’s [52] definition that the model is linear if the linear predictor is optimal. This assumption seems to be the minimum requirement. This means that the residual sequence et fulfils the following conditions:
$$ {\text{E}}\left( {e_t \left| {F_{t - 1} } \right.} \right) = 0,{\text{E}}\left( {e_t^2 |F_{t - 1} } \right) = \sigma ^2 , $$
(5.1)

Keywords

Linear Predictor Bilinear Model Residual Series Noncentrality Parameter Fourth Order Moment 
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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