Financial time series are often non-negative-valued (volumes, trades, durations, realized volatility, daily range) and exhibit clustering. When joint dynamics is of interest, the vector multiplicative error model (vMEM; the element-by-element 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-by-equation approach. A vMEM on several measures of volatility justifies a joint approach revealing full interdependence.
