scholarly journals Fractal approach towards power-law coherency to measure cross-correlations between time series

2017 ◽  
Vol 50 ◽  
pp. 193-200 ◽  
Author(s):  
Ladislav Kristoufek
Keyword(s):  
Time Series ◽  
Power Law ◽  
Fractal Approach ◽  
Cross Correlations

scholarly journals Network Analysis of Cross-Correlations on Forex Market during Crises. Globalisation on Forex Market

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 352
Author(s):  
Janusz Miśkiewicz
Keyword(s):  
Time Series ◽  
Network Analysis ◽  
Exchange Rates ◽  
Power Law ◽  
Financial Crises ◽  
Classification Scheme ◽  
Significant Growth ◽  
Cross Correlations

Within the paper, the problem of globalisation during financial crises is analysed. The research is based on the Forex exchange rates. In the analysis, the power law classification scheme (PLCS) is used. The study shows that during crises cross-correlations increase resulting in significant growth of cliques, and also the ranks of nodes on the converging time series network are growing. This suggests that the crises expose the globalisation processes, which can be verified by the proposed analysis.

MODELING CROSS-CORRELATIONS OF TRAFFIC FLOW

2010 ◽  
Vol 20 (10) ◽  
pp. 3323-3328 ◽  
Author(s):  
PENGJIAN SHANG ◽  
KEQIANG DONG ◽  
SANTI KAMAE
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Power Law ◽  
Cross Correlation ◽  
Heavy Tails ◽  
Fluctuation Analysis ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
Large Increment ◽  
Active Research

The study of diverse natural and nonstationary signals has recently become an area of active research for physicists. This is because these signals exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails and fractality. The focus of the present paper is on the intriguing power-law autocorrelations and cross-correlations in traffic series. Detrended Cross-Correlation Analysis (DCCA) is used to study the traffic flow fluctuations. It is demonstrated that the time series, observed on the Anhua-Bridge highway in the Beijing Third Ring Road (BTRR), may exhibit power-law cross-correlations when they come from two adjacent sections or lanes. This indicates that a large increment in one traffic variable is more likely to be followed by large increment in the other traffic variable. However, for traffic time series derived from nonadjacent sections or lanes, we find that even though they are power-law autocorrelated, there is no cross-correlation between them with a unique exponent. Our results show that DCCA techniques based on Detrended Fluctuation Analysis (DFA) can be used to analyze and interpret the traffic flow.

scholarly journals Spatial and Temporal Spread of the COVID-19 Pandemic Using Self Organizing Neural Networks and a Fuzzy Fractal Approach

2021 ◽  
Vol 13 (15) ◽  
pp. 8295
Author(s):  
Patricia Melin ◽  
Oscar Castillo
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Temporal Trends ◽  
Main Idea ◽  
Temporal Analysis ◽  
Virus Propagation ◽  
Self Organizing Maps ◽  
Fractal Approach ◽  
The Times ◽  
Self Organizing

In this article, the evolution in both space and time of the COVID-19 pandemic is studied by utilizing a neural network with a self-organizing nature for the spatial analysis of data, and a fuzzy fractal method for capturing the temporal trends of the time series of the countries considered in this study. Self-organizing neural networks possess the capability to cluster countries in the space domain based on their similar characteristics, with respect to their COVID-19 cases. This form enables the finding of countries that have a similar behavior, and thus can benefit from utilizing the same methods in fighting the virus propagation. In order to validate the approach, publicly available datasets of COVID-19 cases worldwide have been used. In addition, a fuzzy fractal approach is utilized for the temporal analysis of the time series of the countries considered in this study. Then, a hybrid combination, using fuzzy rules, of both the self-organizing maps and the fuzzy fractal approach is proposed for efficient coronavirus disease 2019 (COVID-19) forecasting of the countries. Relevant conclusions have emerged from this study that may be of great help in putting forward the best possible strategies in fighting the virus pandemic. Many of the existing works concerned with COVID-19 look at the problem mostly from a temporal viewpoint, which is of course relevant, but we strongly believe that the combination of both aspects of the problem is relevant for improving the forecasting ability. The main idea of this article is combining neural networks with a self-organizing nature for clustering countries with a high similarity and the fuzzy fractal approach for being able to forecast the times series. Simulation results of COVID-19 data from countries around the world show the ability of the proposed approach to first spatially cluster the countries and then to accurately predict in time the COVID-19 data for different countries with a fuzzy fractal approach.

Cross-Correlations in the Brownian Motion of Colloidal Nanoparticles

2020 ◽  
Vol 65 (1-2) ◽  
pp. 27-34
Author(s):  
Sz. Kelemen ◽  
◽  
L. Varga ◽  
Z. Néda ◽  
◽  
...  
Keyword(s):  
Brownian Motion ◽  
Power Law ◽  
Cross Correlation ◽  
Colloidal Particles ◽  
Pearson Correlation ◽  
Transverse Component ◽  
Collective Effects ◽  
Colloidal Nanoparticles ◽  
Diffusive Motion ◽  
Cross Correlations

"The two-body cross-correlation for the diffusive motion of colloidal nano-spheres is experimentally investigated. Polystyrene nano-spheres were used in a very low concentration suspension in order to minimize the three- or more body collective effects. Beside the generally used longitudinal and transverse component correlations we investigate also the Pearson correlation in the magnitude of the displacements. In agreement with previous studies we find that the longitudinal and transverse component correlations decay as a function of the inter-particle distance following a power-law trend with an exponent around -2. The Pearson correlation in the magnitude of the displacements decay also as a power-law with an exponent around -1. Keywords: colloidal particles, Brownian motion, cross-correlation. "

scholarly journals Breakdown coefficients and scaling properties of rain fields

1998 ◽  
Vol 5 (2) ◽  
pp. 93-104 ◽  
Author(s):  
D. Harris ◽  
M. Menabde ◽  
A. Seed ◽  
G. Austin
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Power Law ◽  
Scale Parameter ◽  
Probability Distributions ◽  
Scaling Analysis ◽  
Scaling Properties ◽  
Power Law Exponent ◽  
Scale Similarity ◽  
Parameter Estimation Techniques

Abstract. The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf) of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter  estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width), σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.

scholarly journals Technical Note: Long-term memory effect in the atmospheric CO<sub>2</sub> concentration at Mauna Loa

2006 ◽  
Vol 6 (6) ◽  
pp. 11957-11970 ◽  
Author(s):  
C. Varotsos ◽  
M.-N. Assimakopoulos ◽  
M. Efstathiou
Keyword(s):  
Carbon Dioxide ◽  
Time Series ◽  
Power Law ◽  
Carbon Dioxide Concentration ◽  
Global Climate Models ◽  
Fluctuation Analysis ◽  
Original Time Series ◽  
Mauna Loa ◽  
Carbon Dioxide Concentrations ◽  
Original Time

Abstract. The monthly mean values of the atmospheric carbon dioxide concentration derived from in-situ air samples collected at Mauna Loa Observatory, Hawaii, during 1958–2004 (the longest continuous record available in the world) are analyzed by employing the detrended fluctuation analysis to detect scaling behavior in this time series. The main result is that the fluctuations of carbon dioxide concentrations exhibit long-range power-law correlations (long memory) with lag times ranging from four months to eleven years, which correspond to 1/f noise. This result indicates that random perturbations in the carbon dioxide concentrations give rise to noise, characterized by a frequency spectrum following a power-law with exponent that approaches to one; the latter shows that the correlation times grow strongly. This feature is pointing out that a correctly rescaled subset of the original time series of the carbon dioxide concentrations resembles the original time series. Finally, the power-law relationship derived from the real measurements of the carbon dioxide concentrations could also serve as a tool to improve the confidence of the atmospheric chemistry-transport and global climate models.

LONG RANGE CORRELATION PROPERTIES OF AFTERSHOCK RELAXATION SIGNALS

Fractals ◽  
1995 ◽  
Vol 03 (04) ◽  
pp. 839-847 ◽  
Author(s):  
A. VESPIGNANI ◽  
A. PETRI ◽  
A. ALIPPI ◽  
G. PAPARO ◽  
M. COSTANTINI
Keyword(s):  
Time Series ◽  
Acoustic Emission ◽  
Statistical Analysis ◽  
Power Spectrum ◽  
Power Law ◽  
Amplitude Distribution ◽  
Relaxation Processes ◽  
Critical Dynamics ◽  
Range Correlation ◽  
Correlation Properties

Relaxation processes taking place after microfracturing of laboratory samples give rise to ultrasonic acoustic emission signals. Statistical analysis of the resulting time series has revealed many features which are characteristic of critical phenomena. In particular, the autocorrelation functions obey a power-law behavior, implying a power spectrum of the kind 1/f. Also the amplitude distribution N(V) of such signals follows a power law, and the obtained exponents are consistent with those found in other experiments: N(V) dV≃V–γ dV, with γ=1.7±0.2. We also analyzed the distribution N(τ) of the delay time τ between two consecutive acoustic emission events. We found that a N(τ) distribution rather close to a power law constitutes a common feature of all the recorded signals. These experimental results can be considered as a striking evidence for a critical dynamics underlying the microfracturing processes.

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