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| Titel |
Efficient Bayesian inference for ARFIMA processes |
| VerfasserIn |
T. Graves, R. B. Gramacy, C. L. E. Franzke, N. W. Watkins |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
2198-5634
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics Discussions ; 2, no. 2 ; Nr. 2, no. 2 (2015-03-27), S.573-618 |
| Datensatznummer |
250115157
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| Publikation (Nr.) |
 copernicus.org/npgd-2-573-2015.pdf |
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| Zusammenfassung |
| Many geophysical quantities, like atmospheric temperature, water levels in
rivers, and wind speeds, have shown evidence of long-range dependence
(LRD). LRD means that these quantities experience non-trivial temporal memory,
which potentially enhances their predictability, but also hampers the
detection of externally forced trends. Thus, it is important to reliably
identify whether or not a system exhibits LRD. In this paper we present
a modern and systematic approach to the inference of LRD. Rather than
Mandelbrot's fractional Gaussian noise, we use the more flexible
Autoregressive Fractional Integrated Moving Average (ARFIMA) model which is
widely used in time series analysis, and of increasing interest in climate
science. Unlike most previous work on the inference of LRD, which is
frequentist in nature, we provide a systematic treatment of Bayesian
inference. In particular, we provide a new approximate likelihood for
efficient parameter inference, and show how nuisance parameters (e.g. short
memory effects) can be integrated over in order to focus on long memory
parameters, and hypothesis testing more directly. We illustrate our new
methodology on the Nile water level data, with favorable comparison to the
standard estimators. |
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