Dataset for: Fractional Gaussian noise: Prior specification and model comparison

Fractional Gaussian noise (fGn) is a self-similar stochastic
process used to model anti-persistent or persistent
dependency structures in observed time series. Properties of the
autocovariance function of fGn are characterised by the Hurst
exponent (H), which in Bayesian contexts typically has been
assigned a uniform prior on the unit interval. This paper argues
why a uniform prior is unreasonable and introduces the use of a
penalised complexity (PC) prior for H. The PC prior is computed
to penalise divergence from the special case of white noise, and
is invariant to reparameterisations. An immediate advantage is
that the exact same prior can be used for the autocorrelation
coefficient φ a first-order autoregressive process AR(1), as
this model also reflects a flexible version of white noise. Within
the general setting of latent Gaussian models, this allows us to
compare an fGn model component with AR(1) using Bayes
factors, avoiding confounding effects of prior choices for the two
hyperparameters H and φ. Among others, this is useful in
climate regression models where inference for underlying linear or
smooth trends depends heavily on the assumed noise model.