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| Titel |
Improved moment scaling estimation for multifractal signals |
| VerfasserIn |
D. Veneziano, P. Furcolo |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 16, no. 6 ; Nr. 16, no. 6 (2009-11-10), S.641-653 |
| Datensatznummer |
250013307
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| Publikation (Nr.) |
 copernicus.org/npg-16-641-2009.pdf |
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| Zusammenfassung |
| A fundamental problem in the analysis of multifractal processes is to
estimate the scaling exponent K(q) of moments of different order q from
data. Conventional estimators use the empirical moments
μ^rq=⟨ | εr(τ)|q⟩ of wavelet
coefficients εr(τ), where τ is location and r is
resolution. For stationary measures one usually considers "wavelets of
order 0" (averages), whereas for functions with multifractal increments one
must use wavelets of order at least 1. One obtains
K^(q)
as the slope
of log( μ^rq) against log(r) over a range of r. Negative
moments are sensitive to measurement noise and quantization. For them, one
typically uses only the local maxima of | εr(τ)|
(modulus maxima methods). For the positive moments, we modify the standard
estimator K^(q) to
significantly reduce its variance at the expense of
a modest increase in the bias. This is done by separately estimating K(q)
from sub-records and averaging the results. For the negative moments, we show
that the standard modulus maxima estimator is biased and, in the case of
additive noise or quantization, is not applicable with wavelets of order 1 or
higher. For these cases we propose alternative estimators. We also consider
the fitting of parametric models of K(q) and show how, by splitting the
record into sub-records as indicated above, the accuracy of standard methods
can be significantly improved. |
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