Comparative analysis of three MCMC methods for estimating GARCH models

Abstract

GARCH model have been considered as an important and widely employed tool to analyse and forecast variance of the financial market. This study develops three MCMC methods, namely adaptive random walk Metropolis, Hamiltonian Monte Carlo, and Independence Chain Metropolis–Hastings algorithms. It is used to estimate GARCH (1,1) under Normal and Student-t distributions for conditional return distribution. Results on real financial market data indicate that the best method is the approach based on the Independence Chain Metropolis–Hastings algorithm.