Fractional Gaussian noise: Prior specification and model comparison
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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.
CitationSørbye SH, Rue H (2017) Fractional Gaussian noise: Prior specification and model comparison. Environmetrics: e2457. Available: http://dx.doi.org/10.1002/env.2457.
SponsorsThe 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.