Bayesian Time Series Modelling and Prediction with Long-Range Dependence

We present a class of models for trend plus stationary component time series, in which the spectral densities of stationary components are represented via non-parametric smoothness priors combined with long-range dependence components. We discuss model tting and computational issues underlying Bayesian inference under such models, and provide illustration in studies of a climatological time series. These models are of interest to address the questions of existence and extent of apparent long-range e ects in time series arising in speci c scienti c applications.