Fractional Gaussian noise: Prior specification and model comparison

• Published in: Environmetrics
• Main Authors: Sørbye, Sigrunn Holbek, Rue, Håvard
• Format: Article in Journal/Newspaper
• Language: English
• Published: Wiley 2017
• Subjects: VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Statistikk: 412; VDP::Mathematics and natural science: 400::Mathematics: 410::Statistics: 412; Arctic
• Online Access: https://hdl.handle.net/10037/13007; https://doi.org/10.1002/env.2457

This is the peer reviewed version of the following article: Sørbye, S. H. & Rue, H. (2017). Fractional Gaussian noise: Prior specification and model comparison. Environmetrics, 1-12., which has been published in final form at: http://doi.org/10.1002/env.2457 . This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions." Fractional Gaussian noise (fGn) is a stationary 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 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 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.