I am trying to estimate the parameters of the GARCH(1,1) model with MCMC method, firstly, I read the paper:
Metropolis Hasting method is used in the article, but the sampler of parameters, I mean the constant, arch parameter and garch parameter for the conditional variance, are sampled from distribution built by an auxiliary distribution. My question is that, as we could build the likelihood function, then why we need to sample from the auxiliary distribution but not sample from a normal distribution and implement the random walk Metropolis Hasting algorithm.
Actually, I have tried the random walk algorithm but all parameters can not convergent, i do not know the reason. But if I fixed two parameters, supposed we know them, then the unknown parameter can be estimated by random walk Metropolis Hasting algorithm well.
New in this field, thanks.