Fractional Gaussian noise: Prior specification and model comparison

Handle URI:
http://hdl.handle.net/10754/626061
Title:
Fractional Gaussian noise: Prior specification and model comparison
Authors:
Sørbye, Sigrunn Holbek ( 0000-0002-5818-1508 ) ; Rue, Haavard ( 0000-0002-0222-1881 )
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(symbol) 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(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Sørbye SH, Rue H (2017) Fractional Gaussian noise: Prior specification and model comparison. Environmetrics: e2457. Available: http://dx.doi.org/10.1002/env.2457.
Publisher:
Wiley-Blackwell
Journal:
Environmetrics
Issue Date:
7-Jul-2017
DOI:
10.1002/env.2457
ARXIV:
arXiv:1611.06399
Type:
Article
ISSN:
1180-4009
Sponsors:
The 20th Century Reanalysis V2c data is provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, U.S.A., from their website (http://www.esrl.noaa.gov/psd/). The authors wish to thank Hege-Beate Fredriksen for valuable discussions and for processing the data to give aggregated data for land and sea-surface temperatures. The authors also acknowledge The Research Council of Norway for financial support, grant numbers 240873 and 239048.
Additional Links:
http://onlinelibrary.wiley.com/doi/10.1002/env.2457/full
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSørbye, Sigrunn Holbeken
dc.contributor.authorRue, Haavarden
dc.date.accessioned2017-10-31T08:12:58Z-
dc.date.available2017-10-31T08:12:58Z-
dc.date.issued2017-07-07en
dc.identifier.citationSørbye SH, Rue H (2017) Fractional Gaussian noise: Prior specification and model comparison. Environmetrics: e2457. Available: http://dx.doi.org/10.1002/env.2457.en
dc.identifier.issn1180-4009en
dc.identifier.doi10.1002/env.2457en
dc.identifier.urihttp://hdl.handle.net/10754/626061-
dc.description.abstractFractional 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(symbol) 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(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.en
dc.description.sponsorshipThe 20th Century Reanalysis V2c data is provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, U.S.A., from their website (http://www.esrl.noaa.gov/psd/). The authors wish to thank Hege-Beate Fredriksen for valuable discussions and for processing the data to give aggregated data for land and sea-surface temperatures. The authors also acknowledge The Research Council of Norway for financial support, grant numbers 240873 and 239048.en
dc.publisherWiley-Blackwellen
dc.relation.urlhttp://onlinelibrary.wiley.com/doi/10.1002/env.2457/fullen
dc.rightsThis is the submitted version of the following article: Fractional Gaussian noise: Prior specification and model comparison, 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 self-archiving.en
dc.subjectAutoregressive processen
dc.subjectBayes factoren
dc.subjectLong-range dependenceen
dc.subjectPC prioren
dc.subjectR-INLAen
dc.titleFractional Gaussian noise: Prior specification and model comparisonen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalEnvironmetricsen
dc.eprint.versionPre-printen
dc.contributor.institutionDepartment of Mathematic and Statistics; UiT The Arctic University of Norway; Tromsø Norwayen
dc.identifier.arxividarXiv:1611.06399-
kaust.authorRue, Haavarden
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