Temporal scaling and infinite variance are two stylized features often seen together in times series of complex systems. We find that because of their infinite moments samples from fractional Lévy flights produce bi-linear scaling functions which may be incorrectly attributed as evidence of...

We present a generalized stochastic Cantor set by means of a simple cut and delete process and discuss the self-similar properties of the arising geometric structure. To increase the flexibility of the model, two free parameters, m and b, are introduced which tune the relative strength of the...

We investigate if known extrinsic and intrinsic factors fully account for the complex features observed in recordings of human activity as measured from forearm motion in subjects undergoing their regular daily routine. We demonstrate that the apparently random forearm motion possesses dynamic...

In this paper we recursively describe the Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs. In particular, we study the Abelian Sandpile Model on these graphs and obtain the generating function of the recurrent configurations. Further, we give some exact...

A major issue in financial economics is the behaviour of stock returns over long horizons. This study provides empirical evidence of the long-range behaviour of various speculative returns. Using different techniques such as R/S and modified R/S analysis, detrended fluctuation analysis (DFA),...

Three-scaled windowed variance methods (standard, linear regression detrended, and bridge detrended) for estimating the Hurst coefficient (H) are evaluated. The Hurst coefficient, with 0 H 1, characterizes self-similar decay in the time-series autocorrelation function. The scaled windowed...

A wide variety of processes are thought to show “long-range persistence”, specifically an autocorrelation function with power-law decay. A variety of methods have been proposed to quantify this power-law decay, and weather and climate systems, among others, have been claimed to show...

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a...

We report an empirical study of the Ibovespa index of the São Paulo Stock Exchange in which we detect the existence of long-range correlations. To analyze our data, we introduce a rescaled variant of the usual detrended fluctuation analysis that allows us to obtain the Hurst exponent through a...

In financial markets, not only prices and returns can be considered as random variables, but also the waiting time between two transactions varies randomly. In the following, we analyse the statistical properties of General Electric stock prices, traded at NYSE, in October 1999. These properties...