Inference on Multivariate ARCH Processes with Large Sizes

22 Pages Posted: 19 Feb 2009

See all articles by Gilles O. Zumbach

Gilles O. Zumbach

Edgelab; Consulting in Financial Engineering

Date Written: January 15, 2009

Abstract

The covariance matrix is formulated in the framework of a linear multivariate ARCH process with long memory, where the natural cross product structure of the covariance is generalized by adding two linear terms with their respective parameter. The residuals of the linear ARCH process are computed using historical data and the (inverse square root of the) covariance matrix. Simple measure of qualities assessing the independence and unit magnitude of the residual distributions are proposed. The salient properties of the computed residuals are studied for three data sets of size 54, 55 and 330. Both new terms introduced in the covariance help in producing uncorrelated residuals, but the residual magnitudes are very different from unity.The large sizes of the inferred residuals are due to the limited information that can be extracted from the empirical data when the number of time series is large, and denotes a fundamental limitation to the inference that can be achieved.

Keywords: Multivariate GARCH processes, covariance matrix, white noise residuals

Suggested Citation

Zumbach, Gilles, Inference on Multivariate ARCH Processes with Large Sizes (January 15, 2009). Available at SSRN: https://ssrn.com/abstract=1346416 or http://dx.doi.org/10.2139/ssrn.1346416

Gilles Zumbach (Contact Author)

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Consulting in Financial Engineering ( email )

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