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    Fractional Gaussian noise: Prior specification and model comparison

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    1611.06399.pdf
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    Type
    Article
    Authors
    Sørbye, Sigrunn Holbek cc
    Rue, Haavard cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2017-07-07
    Permanent link to this record
    http://hdl.handle.net/10754/626061
    
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    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.
    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.
    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.
    Publisher
    Wiley
    Journal
    Environmetrics
    DOI
    10.1002/env.2457
    arXiv
    1611.06399
    Additional Links
    http://onlinelibrary.wiley.com/doi/10.1002/env.2457/full
    Relations
    Is Supplemented By:
    • [Dataset]
      . DOI: 10.6084/m9.figshare.5134816 HANDLE: 10754/662376
    Is Supplemented By:
    • [Dataset]
      . DOI: 10.6084/m9.figshare.c.3808018 HANDLE: 10754/663918
    ae974a485f413a2113503eed53cd6c53
    10.1002/env.2457
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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