Bayesian semiparametric analysis of vector Multiplicative Error Models

The purpose of our research is to generalize the semiparametric Bayesian MEM of Mira and Solgi (2013) to a multivariate setting, namely vector MEM (vMEM). In the proposed vMEM, given the information set available at time t-1, the positive data vector at time t is modeled as the element-by-element product of a conditional mean vector and a random vector of innovations. In our approach, the process of innovations is an i.i.d. vector process from a unit mean multivariate distribution supported on the positive orthant. We model this distribution nonparametrically, using a Dirichlet process mixture of multivariate log-Normal distributions. We also propose a general parametric model for the conditional mean that nests most of the specifications used in the vMEM literature. To perform Bayesian inference we first expand the parameter space, considering an unidentifiable model with a non-unit mean parameter for the innovations. We then apply the slice sampler algorithm described in Kalli et. al (2011) to the parameter-expanded model and finally post-process this sample to obtain a sample from the posterior of original model. We finally present simulations with different specifications of the conditional mean vector and a real-data application.