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IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 10, OCTOBER 2007 4811 Multifractality Tests Using Bootstrapped
 

Summary: IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 10, OCTOBER 2007 4811
Multifractality Tests Using Bootstrapped
Wavelet Leaders
Herwig Wendt, Member, IEEE, and Patrice Abry
Abstract--Multifractal analysis, which mostly consists of mea-
suring scaling exponents, is becoming a standard technique
available in most empirical data analysis toolboxes. Making use of
the most recent theoretical results, it is based here on the estimation
of the cumulants of the log of the wavelet Leaders, an elaboration
on the wavelet coefficients. These log-cumulants theoretically
enable discrimination between mono- and multifractal processes,
as well as between simple log-normal multifractal models and
more advanced ones. The goal of the present contribution is to
design nonparametric bootstrap hypothesis tests aiming at testing
the nature of the multifractal properties of stochastic processes
and empirical data. Bootstrap issues together with six declinations
of test designs are analyzed. Their statistical performance (signifi-
cances, powers, and p-values) are assessed and compared by means
of Monte Carlo simulations performed on synthetic stochastic
processes whose multifractal properties (and log-cumulants) are

  

Source: Abry, Patrice - Laboratoire de Physique, Ecole Normale Supérieure de Lyon

 

Collections: Engineering