Abstract
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 language | English (US) |
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Article number | e2457 |
Journal | Environmetrics |
Volume | 29 |
Issue number | 5-6 |
DOIs | |
State | Published - Aug 1 2018 |
Bibliographical note
Publisher Copyright:Copyright © 2017 John Wiley & Sons, Ltd.
Keywords
- Autoregressive process
- Bayes factor
- PC prior
- R-INLA
- long-range dependence
ASJC Scopus subject areas
- Statistics and Probability
- Ecological Modeling
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Dataset for: Fractional Gaussian noise: Prior specification and model comparison
Sørbye, S. H. (Creator), Rue, H. (Creator) & Sørbye, S. H. (Creator), figshare, Jun 21 2017
DOI: 10.6084/m9.figshare.5134816, http://hdl.handle.net/10754/662376
Dataset
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Dataset for: Fractional Gaussian noise: Prior specification and model comparison
Sørbye, S. H. (Creator), Rue, H. (Creator) & Sørbye, S. H. (Creator), figshare, 2017
DOI: 10.6084/m9.figshare.c.3808018, http://hdl.handle.net/10754/663918
Dataset