On the Univariate Representation of Multivariate Volatility Models with Common Factors
AbstractFirst, we investigate the minimal 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 imply individual processes with a lot of persistence in the form of long order lags. We show that in the presence of factors, parsimonious univariate representations (e.g. GARCH(1,1)) can result from large multivariate models generating the conditional variances and conditional correlations. Second, we propose an approach to use empirical results for these univariate processes in the analysis of the underlying multivariate, possibly high-dimensional, GARCH process. We use reduced rank procedures to discriminate between a system with seemingly unrelated assets (e.g. a diagonal model) from a set of series with few common sources of volatility. Among the analyzed procedures, the cannonical correlation test statistics on logs of squared returns proposed by Engle and Marcucci (2006) has quite good properties even in the case of falsely omitted cross-moments. Out of 30 returns 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 a single common volatility factor drives these six series.
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Bibliographic InfoPaper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 011.
Date of creation: 2011
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financial economics and financial management ;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-02-26 (All new papers)
- NEP-ECM-2011-02-26 (Econometrics)
- NEP-ETS-2011-02-26 (Econometric Time Series)
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