A Model for Multivariate Non-Negative Valued Processes in Financial Econometrics

The Multiplicative Error Model introduced by Engle (2002) for non-negative valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with positive support. In this paper we propose a multivariate extension of such a model, by taking into consideration the possibility that the vector innovation process be contemporaneously correlated. The estimation procedure is hindered by the lack of probability density functions for multivariate non-negative valued random variables. We suggest the use of copula functions to jointly estimate the parameters of the scale factors and of the correlations of the innovation processes. We illustrate the feasibility of the procedure and the gains over the equation by equation approach using a four variable fully interdependent model with different volatility measures.