Bayesian estimation of Gegenbauer long memory processes with stochastic volatility: methods and applications

This paper discusses a time series model which has generalized long memory in the mean process with stochastic volatility errors and develops a new Bayesian posterior simulator that couples advanced posterior maximisation techniques, as well as traditional latent stochastic volatility estimation procedures. Details are provided on the estimation process, data simulation, and out of sample performance measures. We conduct several rigorous simulation studies and verify our results for in and out of sample behaviour. We further compare the goodness of fit of the generalized process to the standard long memory model by considering two empirical studies on the US Consumer Price Index (CPI) and the US equity risk premium (ERP).