An approximate fractional Gaussian noise model with O(n) computational cost
Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionStatistics Program
Date
2018-11-16Preprint Posting Date
2017-09-18Print Publication Date
2019-07Permanent link to this record
http://hdl.handle.net/10754/630196
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Show full item recordAbstract
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 NatureJournal
Statistics and ComputingarXiv
1709.06115Additional Links
http://link.springer.com/article/10.1007/s11222-018-9843-1ae974a485f413a2113503eed53cd6c53
10.1007/s11222-018-9843-1