Vector Multiplicative Error Models: Representation and Inference
The Multiplicative Error Model introduced by Engle (2002) for positive 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 multi-variate 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 positive valued random variables. We suggest the use of copulafunctions and of estimating equations to jointly estimate the parameters of the scale factors and of the correlations of the innovation processes. Empirical applications on volatility indicators are used to illustrate the gains over the equation by equation procedure.
We thank Christian T. Brownlees, Marco J. Lombardi and Margherita Velucchi for many discussions on MEMs and multivariate extensions, as well as participants in seminars at CORE and IGIER-Bocconi for helpful comments. The usual disclaimer applies. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.