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When joint dynamics is of interest, the vector multiplicative error model (vMEM; the element\u2010by\u2010element product of a vector of conditionally autoregressive scale factors and a multivariate i.i.d. innovation process) is a suitable strategy. Its parameters can be estimated by generalized method of moments, bypassing the problem of specifying a multivariate distribution for the errors. Simulated results show the gains in efficiency relative to an equation\u2010by\u2010equation approach. A vMEM on several measures of volatility justifies a joint approach revealing full interdependence. 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