Bayesian estimation of GARCH model with an adaptive proposal density

TL;DR

This paper introduces an adaptive proposal density scheme for Bayesian GARCH model estimation, significantly reducing autocorrelation times and improving inference efficiency using MCMC methods.

Contribution

It proposes a novel adaptive construction scheme with a Student's t-distribution proposal density for Bayesian GARCH estimation, enhancing sampling efficiency.

Findings

Autocorrelation times are significantly reduced.

The adaptive scheme improves sampling efficiency.

The method is effective for US Dollar/Japanese Yen exchange rate data.

Abstract

A Bayesian estimation of a GARCH model is performed for US Dollar/Japanese Yen exchange rate by the Metropolis-Hastings algorithm with a proposal density given by the adaptive construction scheme. In the adaptive construction scheme the proposal density is assumed to take a form of a multivariate Student's t-distribution and its parameters are evaluated by using the sampled data and updated adaptively during Markov Chain Monte Carlo simulations. We find that the autocorrelation times between the data sampled by the adaptive construction scheme are considerably reduced. We conclude that the adaptive construction scheme works efficiently for the Bayesian inference of the GARCH model.