This paper presents the multifractal model of asset returns (“MMAR”), based upon the pioneering research into multifractal measures by Mandelbrot (1972, 1974). The multifractal model incorporates two elements of Mandelbrot’s past research that are now well-known in finance. First, the MMAR contains long-tails, as in Mandelbrot (1963), which focused on Lévy-stable distributions. In contrast to M...

Résumé Dans cet article nous allons présenter une méthode de détection d’objets basée sur l’analyse multifractale. La détection d’objets est particulièrement difficile lorsque l’on ne connaît pas les caractéristiques des objets pouvant être présents dans l’image. Contrairement aux méthodes le plus souvent proposées, cette méthode est destinée à détecter des objets artificiels dans des images ph...

The discovery of long-range dependence (a kind of asymptotic fractal scaling) in packet data from LANs and WANs, was followed by further work detailing evidence for multifractal behaviour in TCP/IP traffic in WANs. In terms of networking however, physical mechanisms for such behaviour have never been convincingly demonstrated, leaving open the question of whether multifractal traffic models are...

the purpose of this study is to identify the effect of ordinary kriging (ok) and inverse distance weighted (idw) estimation methods for the delineation of mineralized zones based on subsurface data using concentration–volume (c–v) multifractal modeling in the dardevey iron ore deposit, ne iran. variograms and anisotropic ellipsoid were generated for the fe distribution by the above estimation m...

We study numerically multifractal properties of two models of one-dimensional quantum maps: a map with pseudointegrable dynamics and intermediate spectral statistics and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of tw...

Multifractal scaling analysis is applied to the growing surfaces of random deposition model. The effect of number of deposited particles and lattice size on multifractal spectra is studied. Three cases of the growing surfaces are considered: (1) Same total number of particles deposited on different square lattice so that the number of particles deposited per surface site is different. (2) Diffe...

The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of nonstationary time series and the long-range correlations of fractal surfaces, which contains a parameter θ determining the position of the detrending window. We develop multifractal detrending moving average (MFDMA) algorithms for the analysis of one-dimensional multifractal measu...

The multifractal detrended fluctuation analysis of time series is able to reveal the presence of longrange correlations and, at the same time, to characterize the self-similarity of the series. The rich information derivable from the characteristic exponents and the multifractal spectrum can be further analyzed to discover important insights about the underlying dynamical process. In this paper...

We discuss a general concept of multifractality, and give a complete description of the multifractal spectra for Gibbs measures on two-dimensional horseshoes. We discuss a multifractal characterization of surface diffeomorphisms.

For hyperbolic diffeomorphisms, we describe the variational properties of the dimension spectrum of equilibrium measures on locally maximal hyperbolic sets, when the measure or the dynamical system are perturbed. We also obtain explicit expressions for the first derivative of the dimension spectra and the associated Legendre transforms. This allows us to establish a local version of multifracta...