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dc.contributor.authorSørbye, Sigrunn Holbek
dc.contributor.authorMyrvoll-Nilsen, Eirik
dc.contributor.authorRue, Haavard
dc.date.accessioned2018-12-05T11:14:21Z
dc.date.available2018-12-05T11:14:21Z
dc.date.issued2018-11-16
dc.identifier.citationSørbye 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.
dc.identifier.issn0960-3174
dc.identifier.issn1573-1375
dc.identifier.doi10.1007/s11222-018-9843-1
dc.identifier.urihttp://hdl.handle.net/10754/630196
dc.description.abstractFractional 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.
dc.publisherSpringer Nature
dc.relation.urlhttp://link.springer.com/article/10.1007/s11222-018-9843-1
dc.rightsArchived with thanks to Statistics and Computing
dc.subjectAutoregressive process
dc.subjectGaussian Markov random field
dc.subjectIntegrated nested Laplace approximation
dc.subjectLong-range dependence
dc.subjectToeplitz matrix
dc.titleAn approximate fractional Gaussian noise model with O(n) computational cost
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStatistics Program
dc.identifier.journalStatistics and Computing
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Mathematics and Statistics, UiT The Arctic University of Norway, Tromsö, 9037, , Norway
dc.identifier.arxivid1709.06115
kaust.personRue, Haavard
refterms.dateFOA2018-12-05T11:17:14Z
dc.date.published-print2019-07
dc.date.posted2017-09-18


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