A Bayesian Semiparametric Multiplicative Error Model With an Application to Realized Volatility

Abstract

A semiparametric multiplicative error model (MEM) is proposed. In traditional MEM, the innovations are typically assumed to be Gamma distributed (with one free parameter that ensures unit mean of the innovations and thus identifiability of the model), however empirical investigations unveil the inappropriateness of this choice. In the proposed approach, the conditional mean of the time series is modeled parametrically, while we model its conditional distribution nonparametrically by Dirichlet process mixture of Gamma distributions. Bayesian inference is performed using Markov chain Monte Carlo simulation. This model is applied to the time series of daily realized volatility of some indices, and is compared to similar parametric models available in the literature. Our simulations and empirical studies show better predictive performance, flexibility, and robustness to misspecification of our Bayesian semiparametric approach. Supplemental materials for this article are available online.

Key Words:

• Dirichlet process mixture model
• Parameter expansion
• Slice sampler

ACKNOWLEDGMENTS

The authors gratefully thank the two referees for their helpful comments and suggestions that improved this manuscript, and Antonio Lijoi and Sonia Petrone for fruitful discussions on the Bayesian nonparametric aspects related to this research line.