joint work with S.Laurent and F. Palm

We determine the minimum univariate representation of some well known n-dimensional conditional volatility models. Simple systems (e.g. a VEC(0,1)) for the joint behaviour of several variables generate individual processes with a lot of persistence, processes that can be erroneously considered as long memory models for the variance. We are also able to explain the presence of parsimonious univariate representations (e.g. GARCH(1,1)) by the presence in multivariate models of factors generating the conditional variances and conditional correlations. We propose simple reduced rank procedures using either a canonical correlation approach or partial least squares. It emerges that these tools are helpful to discriminate between a system with independent assets (e.g. diagonal BEKK) from a group of series in which common volatility factors are present. Out of 50 retuns from the NYSE, six returns are shown to display a parsimonious GARCH(1,1) model for their conditional variance. We do not reject the hypothesis that single common volatility factor drives these series.

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