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    An approximate fractional Gaussian noise model with O(n) computational cost

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    Type
    Article
    Authors
    Sørbye, Sigrunn Holbek cc
    Myrvoll-Nilsen, Eirik
    Rue, Haavard cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2018-11-16
    Preprint Posting Date
    2017-09-18
    Print Publication Date
    2019-07
    Permanent link to this record
    http://hdl.handle.net/10754/630196
    
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    Abstract
    Fractional Gaussian noise (fGn) is a stationary time series model with long-memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length n using a likelihood-based approach is O(n) , exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to O(n). This paper presents an approximate fGn model of O(n) computational cost, both with direct and indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive (AR) processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four AR components. Specifically, the given approximate fGn model is incorporated within the class of latent Gaussian models in which Bayesian inference is obtained using the methodology of integrated nested Laplace approximation. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.
    Citation
    Sørbye SH, Myrvoll-Nilsen E, Rue H (2018) An approximate fractional Gaussian noise model with O(n) computational cost. Statistics and Computing. Available: http://dx.doi.org/10.1007/s11222-018-9843-1.
    Publisher
    Springer Nature
    Journal
    Statistics and Computing
    DOI
    10.1007/s11222-018-9843-1
    arXiv
    1709.06115
    Additional Links
    http://link.springer.com/article/10.1007/s11222-018-9843-1
    ae974a485f413a2113503eed53cd6c53
    10.1007/s11222-018-9843-1
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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