An Adaptive Markov Chain Monte Carlo Method for GARCH Model

TL;DR

This paper introduces an adaptive MCMC method that constructs a proposal density for GARCH models, significantly reducing autocorrelations and improving simulation efficiency.

Contribution

It presents a novel adaptive proposal density construction technique that enhances MCMC sampling efficiency for GARCH models.

Findings

Autocorrelations are greatly reduced with the adaptive method.

The adaptive approach improves MCMC simulation efficiency.

The method works well for GARCH model sampling.

Abstract

We propose a method to construct a proposal density for the Metropolis-Hastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of the GARCH model. The proposal density is constructed adaptively by using the data sampled by the MCMC metho d itself. It turns out that autocorrelations between the data generated with our adaptive proposal density are greatly reduced. Thus it is concluded that the adaptive construction method is very efficient and works well for the MCMC simulations of the GARCH model.