Related papers: Fractal and Multifractal Time Series
Shape is one of the most important visual attributes to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape…
Attributes which are infrequently expressed in a population can require weeks or months of counting to reach statistical significance. But replacement in a stable population increases long-term counts to a degree determined by the…
We study the multifractal temporal scaling properties of river discharge and precipitation records. We compare the results for the multifractal detrended fluctuation analysis method with the results for the wavelet transform modulus maxima…
We develop a rigorously controlled multi-time scale averaging technique; the averaging is done on a finite time interval, properly chosen, and then, via iterations and normal form transformations, the time intervals are scaled to arbitrary…
Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…
A type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimension can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connect between…
Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical…
Fractal structures naturally emerge in quantum systems whose initial states exhibit spatial discontinuities, a phenomenon first identified by Berry in the paradigmatic case of a particle confined in an infinite potential well. While…
The fluctuations in the particle size distribution for processes of fragmentation and aggregation are studied for stationary state regimes. The system is described in terms of a stochastic process over an adequate tree structure. The RMS…
In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…
The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability…
This article studies the financial time series data processing for machine learning. It introduces the most frequent scaling methods, then compares the resulting stationarity and preservation of useful information for trend forecasting. It…
We develop a powerful yet simple method that generates multifractal fields with fully controlled scaling properties. Adopting the Multifractal Random Walk (MRW) model of Bacry et al. (2001), synthetic multifractal fields are obtained from…
Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to…
Based on the well-known Detrended Fluctuation Analysis (DFA) for time series, in this work we describe a DFA for continuous real variable functions. Under certain conditions, DFA accurately predicts the long-term auto-correlation of the…
We propose to verify relations between quantities which characterize scaling properties of high energy density fluctuations in terms of factorial moments and newly introduced associated frequency moments. Typical examples are presented in…
We use the methodology of singular spectrum analysis (SSA), principal component analysis (PCA), and multi-fractal detrended fluctuation analysis (MFDFA), for investigating characteristics of vibration time series data from a friction brake.…
Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived…
The fractal distribution of charged particles is considered. An example of this distribution is the charged particles that are distributed over fractal. The fractional integrals are used to describe fractal distribution. These integrals are…
Time-frequency representations are important for the analysis of time series. We have developed an online time-series analysis system and equipped it to reliably handle re-alignment in the time-frequency plane. The system can deal with…