41 research outputs found
Fractal Dimensionof the El Salvador Earthquake (2001) time Series
We have estimated multifractal spectrum of the El Salvador earthquake signal
recorded at different locations.Comment: multifractal analysi
A multifractal random walk
We introduce a class of multifractal processes, referred to as Multifractal
Random Walks (MRWs). To our knowledge, it is the first multifractal processes
with continuous dilation invariance properties and stationary increments. MRWs
are very attractive alternative processes to classical cascade-like
multifractal models since they do not involve any particular scale ratio. The
MRWs are indexed by few parameters that are shown to control in a very direct
way the multifractal spectrum and the correlation structure of the increments.
We briefly explain how, in the same way, one can build stationary multifractal
processes or positive random measures.Comment: 5 pages, 4 figures, uses RevTe
Multifractal stationary random measures and multifractal random walks with log-infinitely divisible scaling laws
We define a large class of continuous time multifractal random measures and
processes with arbitrary log-infinitely divisible exact or asymptotic scaling
law. These processes generalize within a unified framework both the recently
defined log-normal Multifractal Random Walk (MRW) [Bacry-Delour-Muzy] and the
log-Poisson "product of cynlindrical pulses" [Barral-Mandelbrot]. Our
construction is based on some ``continuous stochastic multiplication'' from
coarse to fine scales that can be seen as a continuous interpolation of
discrete multiplicative cascades. We prove the stochastic convergence of the
defined processes and study their main statistical properties. The question of
genericity (universality) of limit multifractal processes is addressed within
this new framework. We finally provide some methods for numerical simulations
and discuss some specific examples.Comment: 24 pages, 4 figure
A Multifractal Analysis of Asian Foreign Exchange Markets
We analyze the multifractal spectra of daily foreign exchange rates for
Japan, Hong-Kong, Korea, and Thailand with respect to the United States Dollar
from 1991 to 2005. We find that the return time series show multifractal
spectrum features for all four cases. To observe the effect of the Asian
currency crisis, we also estimate the multifractal spectra of limited series
before and after the crisis. We find that the Korean and Thai foreign exchange
markets experienced a significant increase in multifractality compared to
Hong-Kong and Japan. We also show that the multifractality is stronge related
to the presence of high values of returns in the series
Accounting for risk of non linear portfolios: a novel Fourier approach
The presence of non linear instruments is responsible for the emergence of
non Gaussian features in the price changes distribution of realistic
portfolios, even for Normally distributed risk factors. This is especially true
for the benchmark Delta Gamma Normal model, which in general exhibits
exponentially damped power law tails. We show how the knowledge of the model
characteristic function leads to Fourier representations for two standard risk
measures, the Value at Risk and the Expected Shortfall, and for their
sensitivities with respect to the model parameters. We detail the numerical
implementation of our formulae and we emphasizes the reliability and efficiency
of our results in comparison with Monte Carlo simulation.Comment: 10 pages, 12 figures. Final version accepted for publication on Eur.
Phys. J.
An optimized algorithm for the evaluation of local singularity exponents in digital signals
International audienceRecent works show that the determination of singularity exponents in images can be useful to assess their information content, and in some cases they can cast additional information about underlying physical processes. However, the concept of singularity exponent is associated to differential calculus and thus cannot be easily translated to a digital context, even using wavelets. In this work we show that a recently patented algorithm allows obtaining precise, meaningful values of singularity exponents at every point in the image by the use of a discretized combinatorial mask, which is an extension of a particular wavelet basis. This mask is defined under the hypothesis that singularity exponents are a measure not only of the degree of regularity of the image, but also of the reconstructibility of a signal from their points
Experimental Analysis of Self-Similarity and Random Cascade Processes: Application to Fully Developed Turbulence Data
In the context of fully developed turbulence, Castaing et al. [10] have recently advocated a description of a random cascade process in terms of a kernel that characterizes the nature of the cascade when going from a scale to a finer scale . We elaborate on a method to estimating, directly from experimental data, the shape of for all scales and . We apply this method to turbulent velocity data and we show that it provides very instructive informations about the soundness of various phenomenological models for the intermittency character of turbulent flows
Intermittency of 1D velocity spatial profiles in turbulence: a magnitude cumulant analysis
PACS. 47.27.Eq Turbulence simulation and modeling – 02.50.-r Probability theory, stochastic processes, and statistics – 47.27.Jv High-Reynolds-number turbulence – 47.53.+n Fractals,