Fractional Gaussian noise: Prior specification and model comparison

Sigrunn Holbek Sørbye, Håvard Rue*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent 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 of 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 the 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.

Original languageEnglish (US)
Article numbere2457
Issue number5-6
StatePublished - Aug 1 2018

Bibliographical note

Publisher Copyright:
Copyright © 2017 John Wiley & Sons, Ltd.


  • Autoregressive process
  • Bayes factor
  • PC prior
  • R-INLA
  • long-range dependence

ASJC Scopus subject areas

  • Statistics and Probability
  • Ecological Modeling


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