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 fitting 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 effects in time series arising in specific scientific applications.

Keywords: Bayesian time series analysis; Non-parametric models; Long memory; Spectral analysis

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