scholarly journals Using Self-Similarity and Renormalization Group to Analyze Time Series

2008 ◽  
Author(s):  
Giovanni Arcioni
Keyword(s):  
Time Series ◽  
Renormalization Group ◽  
Self Similarity ◽  
Analyze Time Series

scholarly journals Renormalization group and fractional calculus methods in a complex world: A review

2021 ◽  
Vol 24 (1) ◽  
pp. 5-53
Author(s):  
Lihong Guo ◽  
YangQuan Chen ◽  
Shaoyun Shi ◽  
Bruce J. West
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Fractional Calculus ◽  
Singular Perturbation ◽  
World View ◽  
Singular Perturbation Theory ◽  
Asymptotic Behavior Of Solutions ◽  
Quantum Field ◽  
Self Similarity ◽  
Way Of Thinking

Abstract The concept of the renormalization group (RG) emerged from the renormalization of quantum field variables, which is typically used to deal with the issue of divergences to infinity in quantum field theory. Meanwhile, in the study of phase transitions and critical phenomena, it was found that the self–similarity of systems near critical points can be described using RG methods. Furthermore, since self–similarity is often a defining feature of a complex system, the RG method is also devoted to characterizing complexity. In addition, the RG approach has also proven to be a useful tool to analyze the asymptotic behavior of solutions in the singular perturbation theory. In this review paper, we discuss the origin, development, and application of the RG method in a variety of fields from the physical, social and life sciences, in singular perturbation theory, and reveal the need to connect the RG and the fractional calculus (FC). The FC is another basic mathematical approach for describing complexity. RG and FC entail a potentially new world view, which we present as a way of thinking that differs from the classical Newtonian view. In this new framework, we discuss the essential properties of complex systems from different points of view, as well as, presenting recommendations for future research based on this new way of thinking.

Runoff Fractal Dimension of Songhua River Basin in Harbin Station Based on Db4 Wavelet

2012 ◽  
Vol 550-553 ◽  
pp. 2537-2540
Author(s):  
Hai Yan Gu ◽  
Yong Wang ◽  
Lei Yu
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
River Basin ◽  
Fractal Theory ◽  
Measurement Methods ◽  
Self Similarity ◽  
Songhua River ◽  
Songhua River Basin ◽  
The Songhua River Basin ◽  
The Songhua River

The wavelet analysis and fractal theory into the analysis of hydrological time series, fluctuations in hydrological runoff sequence given the complexity of the measurement methods--- fractal dimension. The real monthly runoffs of 28 years from Songhua River basin in Harbin station are selected as research target. Wavelet transform combined with spectrum method is used to calculate the fractal dimension of runoff. Moreover, the result demonstrates that the runoff in Songhua River basin has the characteristic of self-similarity, and the complexity of runoff in the Songhua River basin in Harbin station is described quantificationally.

Influences of Embedding Parameters and Segment Sizes in Recursive Characteristics Analysis on Coefficients of Friction

2021 ◽  
Vol 31 (04) ◽  
pp. 2150058
Author(s):  
Guodong Sun ◽  
Chao Zhang ◽  
Hua Zhu ◽  
Shihui Lang
Keyword(s):  
Time Series ◽  
Dynamical Evolution ◽  
Chaotic Time Series ◽  
Computational Time ◽  
Data Sets ◽  
Self Similarity ◽  
Tribological Behaviors ◽  
Characteristics Analysis ◽  
Quantification Analysis ◽  
Recursive Matrix

The methods of recurrence plots (RPs) and recurrence quantification analysis (RQA) have been used to investigate the tribosystem. The morphology of RPs and RQA measures are strongly dependent on the embedding parameters of the recursive matrix and the segment sizes of the time-series. To improve the calculation accuracy of recursive characteristics analysis, the influences of the embedding parameters and segment sizes on the morphology of RPs and RQA measures have been studied in this letter. Three kinds of theoretical chaotic time-series and measured coefficient of friction (COF) signals during the running-in process were chosen as research objects, and the morphology of RPs and RQA measures were obtained using CRP toolbox afterward. The results indicate that no embedding was actually needed if the data sets are to be qualitatively analyzed using RPs and RQA. Additionally, the morphology of RPs and RQA measures are sensitive to the segment sizes for theoretical chaotic time-series, while the RQA measures of COF signal in the steady-state period are rather stable due to its self-similarity. Finally, according to the guidelines of the parameter settings, the dynamical evolution of measured COF signals during the running-in process have been investigated. It is indicated that recursive characteristics of COF signals could reveal the tribological behaviors’ evolution and conduct the running-in status identification. The results in this paper are significant for improving the calculation accuracy and saving computational time when using the method of recursive characteristics analysis on the tribological behaviors.

Multiscale Fractional Cumulative Residual Entropy of Higher-Order Moments for Estimating Uncertainty

2020 ◽  
Vol 19 (04) ◽  
pp. 2050038
Author(s):  
Keqiang Dong ◽  
Xiaofang Zhang
Keyword(s):  
Time Series ◽  
Logistic Map ◽  
Higher Order ◽  
Stationary Time Series ◽  
Residual Entropy ◽  
Third Order ◽  
Cumulative Residual Entropy ◽  
Cumulative Residual ◽  
Simulated Time ◽  
Analyze Time Series

The fractional cumulative residual entropy is not only a powerful tool for the analysis of complex system, but also a promising way to analyze time series. In this paper, we present an approach to measure the uncertainty of non-stationary time series named higher-order multiscale fractional cumulative residual entropy. We describe how fractional cumulative residual entropy may be calculated based on second-order, third-order, fourth-order statistical moments and multiscale method. The implementation of higher-order multiscale fractional cumulative residual entropy is illustrated with simulated time series generated by uniform distribution on [0, 1]. Finally, we present the application of higher-order multiscale fractional cumulative residual entropy in logistic map time series and stock markets time series, respectively.

Measuring the self-similarity exponent in Lévy stable processes of financial time series

2013 ◽  
Vol 392 (21) ◽  
pp. 5330-5345 ◽  
Author(s):  
M. Fernández-Martínez ◽  
M.A. Sánchez-Granero ◽  
J.E. Trinidad Segovia
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
The Self ◽  
Stable Processes ◽  
Self Similarity ◽  
Financial Time

scholarly journals Fractional Laplace motion

2006 ◽  
Vol 38 (02) ◽  
pp. 451-464 ◽  
Author(s):  
T. J. Kozubowski ◽  
M. M. Meerschaert ◽  
K. Podgórski
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Hydraulic Conductivity ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Self Similarity ◽  
One Dimensional ◽  
Financial Time

Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional distributions are more peaked at the mode than is a Gaussian distribution, and their tails are heavier. In this paper we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.

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