A Bayesian Semiparametric Vector Multiplicative Error Model

TL;DR

This paper introduces a Bayesian semiparametric extension to the vector Multiplicative Error Model, allowing more flexible modeling of positive-valued time series interactions, with improved fit and prediction.

Contribution

It develops a novel Bayesian semiparametric framework for vMEM, overcoming distributional restrictions and computational challenges, enhancing modeling flexibility and predictive accuracy.

Findings

Outperforms classical vMEM in fitting and prediction

Flexible modeling of innovation distribution achieved

Effective computational approach via slice sampling

Abstract

Interactions among multiple time series of positive random variables are crucial in diverse financial applications, from spillover effects to volatility interdependence. A popular model in this setting is the vector Multiplicative Error Model (vMEM) which poses a linear iterative structure on the dynamics of the conditional mean, perturbed by a multiplicative innovation term. A main limitation of vMEM is however its restrictive assumption on the distribution of the random innovation term. A Bayesian semiparametric approach that models the innovation vector as an infinite location-scale mixture of multidimensional kernels with support on the positive orthant is used to address this major shortcoming of vMEM. Computational complications arising from the constraints to the positive orthant are avoided through the formulation of a slice sampler on the parameter-extended unconstrained version of the model. The method is applied to simulated and real data and a flexible specification is obtained that outperforms the classical ones in terms of fitting and predictive power.