On the Univariate Representation of BEKK Models with Common Factors

Alain Hecq, Sébastien Laurent and Franz Palm

Journal of Time Series Econometrics, 2016, vol. 8, issue 2, 91-113

Abstract: Simple low order multivariate GARCH models imply marginal processes with a lot of persistence in the form of high order lags. This is not what we find in many situations however, where parsimonious univariate GARCH(1,1) models for instance describe quite well the conditional volatility of some asset returns. In order to explain this paradox, we show that in the presence of common GARCH factors, parsimonious univariate representations can result from large multivariate models generating the conditional variances and conditional covariances/correlations. The diagonal model without any contagion effects in conditional volatilities gives rise to similar conclusions though. Consequently, after having extracted a block of assets representing some form of parsimony, remains the task of determining if we have a set of independent assets or instead a highly dependent system generated with a few factors. To investigate this issue, we first evaluate a reduced rank regressions approach for squared returns that we extend to cross-returns. Second we investigate a likelihood ratio approach, where under the null the matrix parameters have a reduced rank structure. It emerged that the latter approach has quite good properties enabling us to discriminate between a system with seemingly unrelated assets (e.g. a diagonal model) and a model with few common sources of volatility.

Keywords: common GARCH; factor models; BEKK; final equations (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (8)

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Related works:
Working Paper: On the Univariate Representation of BEKK Models with Common Factors (2016)
Working Paper: On the univariate representation of BEKK models with common factors (2012)
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DOI: 10.1515/jtse-2015-0002

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