Related papers: Scaling and crossover phenomena in anomalous heliu…
We use some fractal analysis methods to study river flow fluctuations. The result of the Multifractal Detrended Fluctuation Analysis (MF-DFA) shows that there are two crossover timescales at $s_{1\times}\sim12$ and $s_{2\times}\sim130$…
Long-range correlation in financial time series reflects the complex dynamics of the stock markets driven by algorithms and human decisions. Our analysis exploits ultra-high frequency order book data from NASDAQ Nordic over a period of…
A recently developed non-linear fluctuating hydrodynamics theory has been quite successful in describing various features of anomalous energy transport. However the diffusion and the noise terms present in this theory are not derived from…
We present a general framework of detrending methods of fluctuation analysis of which detrended fluctuation analysis (DFA) is one prominent example. Another more recently introduced method is detrending moving average (DMA). Both methods…
Detrend fluctuation analysis (DFA) has become a choice method for effective analysis of a broad variety of nonstationary signals. We show in the present article that, provided the nonstationary fluctuations occur at a large enough time…
Non-equilibrium diffusive systems are known to exhibit long-range correlations, which decay like the inverse 1/L of the system size L in one dimension. Here, taking the example of the ABC model, we show that this size dependence becomes…
Event-by-event fluctuations of hadronic patterns in heavy-ion collisions are studied in search for signatures of quark-hadron phase transition. Attention is focused on a narrow strip in the azimuthal angle with small $\Delta y$. The…
In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first…
In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) $<F_i>$ of the $i$th node and its variance $\sigma_i$ as $\sigma_i \propto < F_{i} >…
The detrended cross-correlation coefficient $\rho_{\rm DCCA}$ has recently been proposed to quantify the strength of cross-correlations on different temporal scales in bivariate, non-stationary time series. It is based on the detrended…
We use, for the first time, the Detrend Fluctuation Analysis (DFA) to study the correlation properties of the transmitted flux fluctuations, in the Lyman-$\alpha$ (Ly$\alpha$) Forest along the lines of sight (LOS) to QSOs, at different…
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…
The scaling function $F(s)$ in detrended fluctuation analysis (DFA) scales as $F(s)\sim s^{H}$ for stochastic processes with Hurst exponents $H$. We prove this scaling law for both stationary stochastic processes with $0<H<1$, and…
Strong anomalous diffusion is {often} characterized by a piecewise-linear spectrum of the moments of displacement. The spectrum is characterized by slopes $\xi$ and $\zeta$ for small and large moments, respectively, and by the critical…
We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). In particular, we present a detailed comparison…
The detrended fluctuation analysis (DFA) is one of the most widely used tools for the detection of long-range correlations in time series. Although DFA has found many interesting applications and has been shown as one of the best performing…
Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture…
An analytical formula for the contributions of the trend leftovers in DFA method is presented, based upon which the crossovers in DFA are investigated in detail. This general formula can explain the calculated results with DFA method for…
Non-statistical event-by-event fluctuations in relativistic heavy-ion collisions have been proposed as a probe of the phase transition of hadronic matter to a deconfined phase of quarks and gluons, the so-called Quark-Gluon Plasma. In a…
Starting from the recognition that hadrons are not produced smoothly at phase transition, the fluctuation of spatial patterns is investigated by finding a measure of the voids that exhibits scaling behavior. The Ising model is used to…