Related papers: Fractal and Multifractal Time Series
Previous studies indicate that nonlinear properties of Gaussian time series with long-range correlations, $u_i$, can be detected and quantified by studying the correlations in the magnitude series $|u_i|$, i.e., the ``volatility''. However,…
In this paper, we use the generalized Hurst exponent approach to study the multi- scaling behavior of different financial time series. We show that this approach is robust and powerful in detecting different types of multiscaling. We…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
This is the transcript of a talk given at the 1992 Complex Systems Summer School. The theory of large fluctuations of stochastically perturbed continuous-time dynamical systems is reviewed, and the large fluctuations of two stochastic…
In this study, we present a method to measure changes over time of fractal dimension. We confirmed that our method can calculate the fractal dimension with the same precision as conventional methods, and tracking performance of our method…
Most data processing techniques, applied to biomedical and sociological time series, are only valid for random fluctuations that are stationary in time. Unfortunately, these data are often non stationary and the use of techniques of…
We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then…
The aim of this review article is to give a comprehensive description of the scaling properties detected for the distribution of cosmic structures. Due to the great variety of statistical methods to describe the large-scale structure of the…
An approach is presented for making predictions about functional time series. The method is applied to data coming from periodically correlated processes and electricity demand, obtaining accurate point forecasts and narrow prediction bands…
Fractals are self-similar recursive structures that have been used in modeling several real world processes. In this work we study how "fractal-like" processes arise in a prediction game where an adversary is generating a sequence of bits…
A two-state master equation based decision making model has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through an inverse power-law probability distribution function in the…
We present some work relating to fractal transformations on masked iterated function systems and demonstrate how well known algorithms for generating fractal transformations can be modifed for these systems. We also demonstrate that these…
The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale…
Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical…
Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal…
We study the statistical fluctuations (such as the variance) of causal set quantities, with particular focus on the causal set action. To facilitate calculating such fluctuations, we develop tools to account for correlations between causal…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…
Multifractal analysis has been used to diagnoze cracked and healthy rotors. Is has been shown that the complexity and regularity criteria of the dynamical systems defined by the multiple scaling of the time series can indicate the damages…
We present a exactly soluble model for financial time series that mimics the long range volatility correlations known to be present in financial data. Although our model is `monofractal' by construction, it shows apparent multiscaling as a…