# An approximate fractional Gaussian noise model with computational cost

Handle URI:
http://hdl.handle.net/10754/626466
Title:
An approximate fractional Gaussian noise model with computational cost
Authors:
Sørbye, Sigrunn H.; Myrvoll-Nilsen, Eirik; Rue, Haavard ( 0000-0002-0222-1881 )
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 ${\mathcal O}(n^{2})$, 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 ${\mathcal O}(n^{3})$. This paper presents an approximate fGn model of ${\mathcal O}(n)$ computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive 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 components. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
arXiv
Issue Date:
18-Sep-2017
ARXIV:
arXiv:1709.06115
Type:
Preprint
http://arxiv.org/abs/1709.06115v1; http://arxiv.org/pdf/1709.06115v1
Appears in Collections:
Other/General Submission; Other/General Submission; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

DC FieldValue Language
dc.contributor.authorSørbye, Sigrunn H.en
dc.contributor.authorMyrvoll-Nilsen, Eiriken
dc.contributor.authorRue, Haavarden
dc.date.accessioned2017-12-28T07:32:11Z-
dc.date.available2017-12-28T07:32:11Z-
dc.date.issued2017-09-18en
dc.identifier.urihttp://hdl.handle.net/10754/626466-
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 ${\mathcal O}(n^{2})$, 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 ${\mathcal O}(n^{3})$. This paper presents an approximate fGn model of ${\mathcal O}(n)$ computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive 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 components. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1709.06115v1en
dc.relation.urlhttp://arxiv.org/pdf/1709.06115v1en
dc.rightsArchived with thanks to arXiven
dc.titleAn approximate fractional Gaussian noise model with computational costen
dc.typePreprinten
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.eprint.versionPre-printen
dc.contributor.institutionDepartment of Mathematical Sciences, UiT The Arctic University of Norway, Tromsø, Norwayen
dc.identifier.arxividarXiv:1709.06115en
kaust.authorRue, Haavarden