Zero Variance and Hamiltonian Monte Carlo Methods in GARCH Models

TL;DR

This paper introduces Bayesian Hamiltonian Monte Carlo methods, including Zero-variance schemes, for more efficient parameter estimation in asymmetric GARCH models, reducing standard errors with minimal additional computational cost.

Contribution

It develops and implements Zero-variance and Hamiltonian Monte Carlo methods tailored for asymmetric GARCH models, enhancing inference efficiency.

Findings

Reduced standard errors in parameter estimates.

Efficient inference with minimal extra computation.

Applicable to models with different error distributions.

Abstract

In this paper, we develop Bayesian Hamiltonian Monte Carlo methods for inference in asymmetric GARCH models under different distributions for the error term. We implemented Zero-variance and Hamiltonian Monte Carlo schemes for parameter estimation to try and reduce the standard errors of the estimates thus obtaing more efficient results at the price of a small extra computational cost.