The Multifractal Embedded Branching Process (MEBP) process and Canonical Embedded Branching Process (CEBP) process were introduced by Decrouez and Jones (2012). The CEBP is a process in which the crossings of dyadic intervals constitute a branching process. An MEBP process is defined as a...

Electronic Cardiogram (ECG) data taken from healthy adult subjects are found to characterize multifractality. In order to quantitatively analyze multifractal spectrum, the area of the spectrum is computed. We have a comparison between the spectrum of the young subjects and that of the old ones....

A time series can be decomposed into two sub-series: a magnitude series and a sign series. Here we analyze separately the scaling properties of the magnitude series and the sign series using the increment time series of cardiac interbeat intervals as an example. We find that time series having...

This paper proposes the generalized use of fractional Brownian motion in a multifractal trading time framework to reveal variation in the index price diffusion process that appears before and after 'extreme' events of distinct origin. "Crashes" following internal self-organization and those...

We consider a self-similar phase space with specific fractal dimension d being distributed with spectrum function f(d). Related thermostatistics is shown to be governed by the Tsallis formalism of the non-extensive statistics, where the non-additivity parameter equals to τ̄(q)≡1/τ(q)1, and...

The surface profiles resulting from a laser beam melt ablation process have been quantified on the basis of the multifractal formalism. The multifractal spectra for several parameters sets, obtained with the wavelet transform modulus maxima method, were found to change towards higher Hölder...

We develop a financial market model using an Ising spin system on a Sierpinski carpet lattice that breaks the equal status of each spin. To study the fluctuation behavior of the financial model, we present numerical research based on Monte Carlo simulation in conjunction with the statistical...

There is a growing awareness among financial researchers that the traditional models of asset returns cannot capture essential time series properties of the current stock return data. We examine commonly used models, such as the autoregressive integrated moving average (ARIMA) and the...