Multivariate ARCH Processes

Gilles Zumbach
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Gilles Zumbach: Consulting in Financial Research

Chapter Chapter 18 in Discrete Time Series, Processes, and Applications in Finance, 2013, pp 273-294 from Springer

Abstract: Abstract With a deep knowledge of the univariate processes and of the covariance matrix, multivariate ARCH processes can be studied. The general multivariate setup is presented. In order to limit the exploding number of parameters, the simplest linear ARCH process is studied first. Due to the very small eigenvalues, the covariance matrix is singular, and a regularization should be introduced in order to compute the empirical innovations. The relationship between the possible regularizations and the statistical properties of the innovations is presented. In a second step, the affine ARCH process is introduced, discussing the specific issues related to the introduction of the mean terms. In a third step, more general multivariate ARCH processes are summarized.

Keywords: Covariance Matrix; Portfolio Optimization; Small Eigenvalue; Stock Index; Zero Eigenvalue (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprfcp:978-3-642-31742-2_18

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DOI: 10.1007/978-3-642-31742-2_18

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