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Multivariate ARCH Models

  • Christian Gouriéroux
Chapter
Part of the Springer Series in Statistics book series (SSS)

Abstract

In chapter 3, we studied univariate processes \( \in = \left( {{ \in _t}} \right) \) satisfying GARCH (p, q) representations. The conditional expectations and variances were defined by
$$ \left\{ {\begin{array}{*{20}{c}} {E\left( {{\varepsilon _t}/{\varepsilon _{t - 1}}} \right) = 0,} \\ {V\left( {{\varepsilon _t}/{\varepsilon _{t - 1}}} \right) = {h_t} = c + \sum\limits_{i = 1}^q {{\alpha _i}\varepsilon _{t - i}^2 + \sum\limits_{j = 1}^p {{\beta _j}{h_{t - j}}.} } } \end{array}} \right. $$

Keywords

Conditional Distribution Conditional Expectation Conditional Variance Spectral Decomposition GARCH Model 
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 1997

Authors and Affiliations

  • Christian Gouriéroux
    • 1
  1. 1.Centre de Recherche en Economie et StatistiqueLaboratoire de Finance-AssuranceMalakoff CedexFrance

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