When common factors strongly influence two power-law cross-correlated time series recorded in complex natural or social systems, using detrended cross-correlation analysis (DCCA) without considering these common factors will bias the results. We use detrended partial cross-correlation analysis (DPXA) to uncover the intrinsic power-law cross correlations between two simultaneously recorded time ...

By applying the multifractal detrended fluctuation analysis to the high-frequency tick-bytick data from Deutsche Börse both in the price and in the time domains, we investigate multifractal properties of the time series of logarithmic price increments and inter-trade intervals of time. We show that both quantities reveal multiscaling and that this result holds across different stocks. The origi...

In this paper, we investigate the queueing behavior of multifractal traffic flows. Initially, we derive a global scaling parameter for multifractal processes. Next, we obtain a global scaling based expression for the effective bandwidth of multifractal flows. Relating this effective bandwidth estimate to the statistical network calculus, we propose performance bounds for high-speed networks. Ou...

The multifractal scaling exponents are calculated for the critical wave function of a two-dimensional Dirac fermion in the presence of a random magnetic field. It is shown that the problem of calculating the multifractal spectrum maps into the thermodynamics of a static particle in a random potential. The multifractal exponents are simply given in terms of thermodynamic functions, such as free ...

We analyze the multifractal spectra of daily foreign exchange rates for Japan, Hong-Kong, Korea, and Thailand with respect to the United States in the period from 1991 until 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 af...

Čerenkov images of air showers can also be classified using multifractal and wavelet parameters, as compared to the conventional Hillas image parameters. This new technique was applied to the images recorded by the cameras of the stereoscopic imaging air Čerenkov-telescopes operated by the HEGRA collaboration. With respect to the identification of particles, the performance of multifractal and ...

By viewing the covers of a fractal as a statistical mechanical system, the exact capacity of a multifractal is computed. The procedure can be extended to any multifractal described by a scaling function to show why the capacity and Hausdorff dimension are expected to be equal.

In this paper we prove that the conjectures of Frisch and Parisi in 9] and Arneodo et al in 1] (called the multifractal formalism for functions) may fail for some non homogenous selfsimilar functions in m dimension, m 2. In these cases, we compute the correct spectrum of singularities and we show how the multifractal formalism must be modiied.

We consider the multifractal spectrum of harmonic measure of a Brownian motion path in two or three dimensions. We show that the multifractal spectrum is nontrivial and relate the spectrum to the intersection exponent. As a corollary we show that harmonic measure on a three dimension Brownian motion path is carried on a set of Hausdorr dimension strictly less than two.

We analyze the fractal behavior of the high frequency part of the Fourier spectrum of fBm using multifractal analysis and show that it is not consistent with what is measured on real traac traces. We propose two extensions of fBm which come closer to actual traac traces multifractal properties.