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| Titel |
Just two moments! A cautionary note against use of high-order moments in multifractal models in hydrology |
| VerfasserIn |
F. Lombardo, E. Volpi, D. Koutsoyiannis, S. M. Papalexiou |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1027-5606
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| Digitales Dokument |
URL |
| Erschienen |
In: Hydrology and Earth System Sciences ; 18, no. 1 ; Nr. 18, no. 1 (2014-01-17), S.243-255 |
| Datensatznummer |
250120255
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| Publikation (Nr.) |
 copernicus.org/hess-18-243-2014.pdf |
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| Zusammenfassung |
| The need of understanding and modelling the space–time variability of
natural processes in hydrological sciences produced a large body of
literature over the last thirty years. In this context, a multifractal
framework provides parsimonious models which can be applied to a wide-scale
range of hydrological processes, and are based on the empirical detection of
some patterns in observational data, i.e. a scale invariant mechanism
repeating scale after scale. Hence, multifractal analyses heavily rely on
available data series and their statistical processing. In such analyses,
high order moments are often estimated and used in model identification and
fitting as if they were reliable. This paper warns practitioners against
the blind use in geophysical time series analyses of classical statistics, which is
based upon independent samples typically following distributions of
exponential type. Indeed, the study of natural processes reveals scaling
behaviours in state (departure from exponential distribution tails) and in
time (departure from independence), thus implying dramatic increase of bias
and uncertainty in statistical estimation. Surprisingly, all these
differences are commonly unaccounted for in most multifractal analyses of
hydrological processes, which may result in inappropriate modelling, wrong
inferences and false claims about the properties of the processes studied.
Using theoretical reasoning and Monte Carlo simulations, we find that the
reliability of multifractal methods that use high order moments
(>3) is questionable. In particular, we suggest that, because of
estimation problems, the use of moments of order higher than two should be
avoided, either in justifying or fitting models. Nonetheless, in most
problems the first two moments provide enough information for the most
important characteristics of the distribution. |
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