A Bayesian MCMC based estimation of Long memory in state space model

To estimate the long memory series in the framework of state space model is rarely documented although the theoretical foundation was well built in late 90s, and the literatures concentrate mainly on the estimation in stationary case. This paper aims to estimate the parameters in a wide range of long memory series by applying approximate Maximum Likelihood Estimation (MLE) and Bayesian Monte Carlo Markov Chain (MCMC) methodology. We show that both methods perform quite well with the exception in the case that the series is nearly non-stationary, where pure MLE gives out seriously over biased estimation and the Bayesian MCMC estimation can avoid this problem when pre-knowledge is available.