scholarly journals A universal mechanism for long-range cross-correlations

2014 ◽  
Vol 105 (2) ◽  
pp. 26004 ◽  
Author(s):  
F. K. Diakonos ◽  
A. K. Karlis ◽  
P. Schmelcher
2007 ◽  
Vol 56 (1) ◽  
pp. 47-52 ◽  
Author(s):  
B. Podobnik ◽  
D. F. Fu ◽  
H. E. Stanley ◽  
P. Ch. Ivanov

2001 ◽  
Vol 1 (2) ◽  
pp. 212-216 ◽  
Author(s):  
J-P. Bouchaud ◽  
I. Giardina ◽  
M. Mzard

2021 ◽  
Author(s):  
Lenin Del Rio Amador ◽  
Shaun Lovejoy

<p>Over time scales between 10 days and 10-20 years – the macroweather regime – atmospheric fields, including the temperature, respect statistical scale symmetries, such as power-law correlations, that imply the existence of a huge memory in the system that can be exploited for long-term forecasts. The Stochastic Seasonal to Interannual Prediction System (StocSIPS) is a stochastic model that exploits these symmetries to perform long-term forecasts. It models the temperature as the high-frequency limit of the (fractional) energy balance equation (fractional Gaussian noise) which governs radiative equilibrium processes when the relevant equilibrium relaxation processes are power law, rather than exponential. They are obtained when the order of the relaxation equation is fractional rather than integer and they are solved as past value problems rather than initial value problems.</p><p>Long-range weather prediction is conventionally an initial value problem that uses the current state of the atmosphere to produce ensemble forecasts. In contrast, StocSIPS predictions for long-memory processes are “past value” problems that use historical data to provide conditional forecasts. Cross-correlations can be used to define teleconnection patterns, and for identifying possible dynamical interactions, but they do not necessarily imply any causation. Using the precise notion of Granger causality, we show that for long-range stochastic temperature forecasts, the cross-correlations are only relevant at the level of the innovations – not temperatures. Extended here to the multivariate case, (m-StocSIPS) produces realistic space-time temperature simulations. Although it has no Granger causality, we are able to reproduce emergent properties including realistic teleconnection networks and El Niño events and indices.</p>


Fractals ◽  
2017 ◽  
Vol 25 (06) ◽  
pp. 1750054 ◽  
Author(s):  
ZHI-QIANG JIANG ◽  
XING-LU GAO ◽  
WEI-XING ZHOU ◽  
H. EUGENE STANLEY

Complex systems are composed of mutually interacting components and the output values of these components usually exhibit long-range cross-correlations. Using wavelet analysis, we propose a method of characterizing the joint multifractal nature of these long-range cross correlations, a method we call multifractal cross wavelet analysis (MFXWT). We assess the performance of the MFXWT method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. For binomial multifractal measures, we find the empirical joint multifractality of MFXWT to be in approximate agreement with the theoretical formula. For bFBMs, MFXWT may provide spurious multifractality because of the wide spanning range of the multifractal spectrum. We also apply the MFXWT method to stock market indices, and in pairs of index returns and volatilities we find an intriguing joint multifractal behavior. The tests on surrogate series also reveal that the cross correlation behavior, particularly the cross correlation with zero lag, is the main origin of cross multifractality.


2008 ◽  
Vol 387 (15) ◽  
pp. 3954-3959 ◽  
Author(s):  
Boris Podobnik ◽  
Davor Horvatic ◽  
Alfonso Lam Ng ◽  
H. Eugene Stanley ◽  
Plamen Ch. Ivanov

Author(s):  
Akio Nakata ◽  
Miki Kaneko ◽  
Chinami Taki ◽  
Naoko Evans ◽  
Taiki Shigematsu ◽  
...  

We propose higher-order detrending moving-average cross-correlation analysis (DMCA) to assess the long-range cross-correlations in cardiorespiratory and cardiovascular interactions. Although the original (zeroth-order) DMCA employs a simple moving-average detrending filter to remove non-stationary trends embedded in the observed time series, our approach incorporates a Savitzky–Golay filter as a higher-order detrending method. Because the non-stationary trends can adversely affect the long-range correlation assessment, the higher-order detrending serves to improve accuracy. To achieve a more reliable characterization of the long-range cross-correlations, we demonstrate the importance of the following steps: correcting the time scale, confirming the consistency of different order DMCAs, and estimating the time lag between time series. We applied this methodological framework to cardiorespiratory and cardiovascular time series analysis. In the cardiorespiratory interaction, respiratory and heart rate variability (HRV) showed long-range auto-correlations; however, no factor was shared between them. In the cardiovascular interaction, beat-to-beat systolic blood pressure and HRV showed long-range auto-correlations and shared a common long-range, cross-correlated factor. This article is part of the theme issue ‘Advanced computation in cardiovascular physiology: new challenges and opportunities’.


2017 ◽  
Vol 114 (13) ◽  
pp. 3322-3327 ◽  
Author(s):  
Boyce Tsang ◽  
Zachary E. Dell ◽  
Lingxiang Jiang ◽  
Kenneth S. Schweizer ◽  
Steve Granick

Entanglement in polymer and biological physics involves a state in which linear interthreaded macromolecules in isotropic liquids diffuse in a spatially anisotropic manner beyond a characteristic mesoscopic time and length scale (tube diameter). The physical reason is that linear macromolecules become transiently localized in directions transverse to their backbone but diffuse with relative ease parallel to it. Within the resulting broad spectrum of relaxation times there is an extended period before the longest relaxation time when filaments occupy a time-averaged cylindrical space of near-constant density. Here we show its implication with experiments based on fluorescence tracking of dilutely labeled macromolecules. The entangled pairs of aqueous F-actin biofilaments diffuse with separation-dependent dynamic cross-correlations that exceed those expected from continuum hydrodynamics up to strikingly large spatial distances of ≈15 µm, which is more than 104 times the size of the solvent water molecules in which they are dissolved, and is more than 50 times the dynamic tube diameter, but is almost equal to the filament length. Modeling this entangled system as a collection of rigid rods, we present a statistical mechanical theory that predicts these long-range dynamic correlations as an emergent consequence of an effective long-range interpolymer repulsion due to the de Gennes correlation hole, which is a combined consequence of chain connectivity and uncrossability. The key physical assumption needed to make theory and experiment agree is that solutions of entangled biofilaments localized in tubes that are effectively dynamically incompressible over the relevant intermediate time and length scales.


2004 ◽  
Vol 07 (07) ◽  
pp. 823-851
Author(s):  
NICOLAS BOITOUT ◽  
LOREDANA URECHE-RANGAU

This paper examines the behavior of volatility and trading volume in an extended Mixture-of-Distribution Hypothesis framework. According to this Hypothesis, both volatility and volume are subordinated to the same latent, stochastic variable: the information flow. One way to enlarge this modeling in order to capture long range dependecies observed in these two variables is to use multi-component volatility models. However, traditional multi-component volatility models seem no longer enough to describe the more complex behavior of the volatility. This is why we introduce in this class of models, a stochastic cascade model of volatility, inherited from the multifractal paradigm. In the empirical section we provide some evidence in favor of this approach. Both volatility and volume are fractionally integrated processes with similar hyperbolic decay rates, but the long range dependence of their power transforms exhibits significant differences. Moreover, we emphasize the existence of lagged cross-correlations between the volatilities at different sampling frequencies, first pointed out by Müller et al. [59], which historically opened the door to a (stochastic) cascade scheme of the volatility in the literature. A multiscaling analysis of the structure functions (generalized volatilities) confirms this result. The empirical results are provided with data on the French stock Alcatel.


2021 ◽  
Author(s):  
Aktham Maghyereh ◽  
hussein abdoh

Abstract In this paper, we exploit multifractal detrended cross-correlation analysis (MF-DCCA) to investigate the impact of COVID-19 pandemic on the cross-correlations between oil and US equity market (as represented by the S&P 500 index). First, we examine the detrended moving average cross-correlation coefficient between oil and S&P 500 returns before and during the COVID-19 pandemic. The correlation analysis shows that US stock markets became more correlated with oil during the pandemic in the long term. Second, we find that the pandemic has caused an increase in the long range cross correlations over the small fluctuations. Third, the MF-DCCA method shows that the pandemic caused an increase of multifractality in cross-correlations between the two markets. In sum, the pandemic caused a closer correlation between oil and US equity in the long range and a deeper dynamical connection between oil and US equity markets as indicated by the multifractality tests.


2015 ◽  
Vol 14 (03) ◽  
pp. 1550023 ◽  
Author(s):  
Yi Yin ◽  
Pengjian Shang

In this paper, we propose multiscale detrended cross-correlation analysis (MSDCCA) to detect the long-range power-law cross-correlation of considered signals in the presence of nonstationarity. For improving the performance and getting better robustness, we further introduce the empirical mode decomposition (EMD) to eliminate the noise effects and propose MSDCCA method combined with EMD, which is called MS-EDXA method, then systematically investigate the multiscale cross-correlation structure of the real traffic signals. We apply the MSDCCA and MS-EDXA methods to study the cross-correlations in three situations: velocity and volume on one lane, velocities on the present and the next moment and velocities on the adjacent lanes, and further compare their spectrums respectively. When the difference between the spectrums of MSDCCA and MS-EDXA becomes unobvious, there is a crossover which denotes the turning point of difference. The crossover results from the competition between the noise effects in the original signals and the intrinsic fluctuation of traffic signals and divides the plot of spectrums into two regions. In all the three case, MS-EDXA method makes the average of local scaling exponents increased and the standard deviation decreased and provides a relative stable persistent scaling cross-correlated behavior which gets the analysis more precise and more robust and improves the performance after noises being removed. Applying MS-EDXA method avoids the inaccurate characteristics of multiscale cross-correlation structure at the short scale including the spectrum minimum, the range for the spectrum fluctuation and general trend, which are caused by the noise in the original signals. We get the conclusions that the traffic velocity and volume are long-range cross-correlated, which is accordant to their actual evolution, while velocities on the present and the next moment and velocities on adjacent lanes reflect the strong cross-correlations both in temporal and spatial dimensions. We also reveal the similarity and uniqueness in the cross-correlation situations between velocities. Besides, signals on one lane show stronger long-range cross-correlation than that on adjacent lanes. Thus, the multiscale cross-correlation structure acquired by MS-EDXA is more close to the intrinsic mechanism of traffic system and reflects more accurate and more abundant traffic information.


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