Bayesian Multivariate Quantile Regression with alternative Time-varying Volatility Specifications

TL;DR

This paper introduces a Bayesian multivariate quantile regression model with time-varying volatility for energy commodities, utilizing stochastic volatility and GARCH processes, and demonstrates improved tail prediction performance.

Contribution

It develops a novel Bayesian multivariate quantile regression framework incorporating time-varying volatility via stochastic volatility and GARCH, with an efficient MCMC estimation method.

Findings

Models outperform homoskedastic benchmarks in tail prediction.

Model combination improves overall predictive performance.

The approach effectively captures tail behavior in energy commodities.

Abstract

This article proposes a novel Bayesian multivariate quantile regression to forecast the tail behavior of energy commodities, where the homoskedasticity assumption is relaxed to allow for time-varying volatility. In particular, we exploit the mixture representation of the multivariate asymmetric Laplace likelihood and the Cholesky-type decomposition of the scale matrix to introduce stochastic volatility and GARCH processes and then provide an efficient MCMC to estimate them. The proposed models outperform the homoskedastic benchmark mainly when predicting the distribution's tails. We provide a model combination using a quantile score-based weighting scheme, which leads to improved performances, notably when no single model uniformly outperforms the other across quantiles, time, or variables.