Determining the Length of the Time Series Sequence for Generating Self-Similar Traffic with the Required Hurst Index

2021 ◽  
Author(s):  
T. M. Tatarnikova ◽  
B. Ya. Sovetov ◽  
V.V. Cehanovsky
Keyword(s):  
Time Series ◽  
Hurst Index ◽  
Self Similar

scholarly journals A Study of Wavelet Analysis and Data Extraction from Second-Order Self-Similar Time Series

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Leopoldo Estrada Vargas ◽  
Deni Torres Roman ◽  
Homero Toral Cruz
Keyword(s):  
Time Series ◽  
Discrete Time ◽  
Close Association ◽  
Second Order ◽  
Basis Functions ◽  
Hurst Index ◽  
Similar Time ◽  
Sample Mean ◽  
Discrete Time Series ◽  
Self Similar

Statistical analysis and synthesis of self-similar discrete time signals are presented. The analysis equation is formally defined through a special family of basis functions of which the simplest case matches the Haar wavelet. The original discrete time series is synthesized without loss by a linear combination of the basis functions after some scaling, displacement, and phase shift. The decomposition is then used to synthesize a new second-order self-similar signal with a different Hurst index than the original. The components are also used to describe the behavior of the estimated mean and variance of self-similar discrete time series. It is shown that the sample mean, although it is unbiased, provides less information about the process mean as its Hurst index is higher. It is also demonstrated that the classical variance estimator is biased and that the widely accepted aggregated variance-based estimator of the Hurst index results biased not due to its nature (which is being unbiased and has minimal variance) but to flaws in its implementation. Using the proposed decomposition, the correct estimation of theVariance Plotis described, as well as its close association with the popularLogscale Diagram.

SLICES OF MULTIFRACTAL MEASURES AND APPLICATIONS TO RAINFALL DISTRIBUTIONS

Fractals ◽  
2000 ◽  
Vol 08 (04) ◽  
pp. 337-348 ◽  
Author(s):  
BIRGER LAMMERING
Keyword(s):  
Time Series ◽  
Field Data ◽  
Rainfall Data ◽  
Rainfall Time Series ◽  
Mathematical Ideas ◽  
Radar Images ◽  
The Usa ◽  
Self Similar ◽  
The Relationship ◽  
Plane Measure

We discuss the relationship between the multifractal functions of a plane measure and those of slices or sections of the measure with a line. Motivated by recent mathematical ideas about the relationship between measures and their slices, we formulate the "slice hypothesis," and consider the theoretical limitations of this hypothesis. We compute the multifractal functions of several standard self-similar and self-affine measures and their slices to examine the validity of the slice hypothesis. We are particularly interested in using the slice hypothesis to estimate multifractal properties of spatial rainfall fields by analyzing rainfall data representing slices of rainfall fields. We consider how rainfall time series at a fixed site and slices of composite radar images can be used for this purpose, testing this on field data from a radar composite in the USA and on appropriate time series.

scholarly journals EFFECTS OF POLYNOMIAL TRENDS ON DETRENDING MOVING AVERAGE ANALYSIS

Fractals ◽  
2015 ◽  
Vol 23 (03) ◽  
pp. 1550034 ◽  
Author(s):  
YING-HUI SHAO ◽  
GAO-FENG GU ◽  
ZHI-QIANG JIANG ◽  
WEI-XING ZHOU
Keyword(s):  
Time Series ◽  
Numerical Experiments ◽  
Moving Average ◽  
Nonstationary Time Series ◽  
Hurst Index ◽  
Forward Algorithm ◽  
Average Analysis ◽  
Polynomial Trends ◽  
Linear Trends

The detrending moving average (DMA) algorithm is one of the best performing methods to quantify the long-term correlations in nonstationary time series. As many long-term correlated time series in real systems contain various trends, we investigate the effects of polynomial trends on the scaling behaviors and the performances of three widely used DMA methods including backward algorithm (BDMA), centered algorithm (CDMA) and forward algorithm (FDMA). We derive a general framework for polynomial trends and obtain analytical results for constant shifts and linear trends. We find that the behavior of the CDMA method is not influenced by constant shifts. In contrast, linear trends cause a crossover in the CDMA fluctuation functions. We also find that constant shifts and linear trends cause crossovers in the fluctuation functions obtained from the BDMA and FDMA methods. When a crossover exists, the scaling behavior at small scales comes from the intrinsic time series while that at large scales is dominated by the constant shifts or linear trends. We also derive analytically the expressions of crossover scales and show that the crossover scale depends on the strength of the polynomial trends, the Hurst index, and in some cases (linear trends for BDMA and FDMA) the length of the time series. In all cases, the BDMA and the FDMA behave almost the same under the influence of constant shifts or linear trends. Extensive numerical experiments confirm excellently the analytical derivations. We conclude that the CDMA method outperforms the BDMA and FDMA methods in the presence of polynomial trends.

scholarly journals The Associative Multifractal Process: A Novel Model for Computer Network Traffic Flows

2021 ◽  
Author(s):  
Ginno Millán ◽  
Gastón Lefranc ◽  
Román Osorio-Comparán
Keyword(s):  
Mathematical Model ◽  
Time Series ◽  
High Speed ◽  
Computer Network ◽  
Traffic Flows ◽  
Multifractal Formalism ◽  
Proposed Model ◽  
Self Similar ◽  
Speed Computer ◽  
Novel Model

A novel constructive mathematical model based on the multifractal formalism in order to accurately characterizing the localized fluctuations present in the course of traffic flows today high-speed computer networks is presented. The proposed model has the target to analyze self-similar second-order time series representative of traffic flows in terms of their roughness and impulsivity.

scholarly journals Fractal-based techniques for physiological time series: An updated approach

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 741-750 ◽  
Author(s):  
José Luis Roca ◽  
German Rodríguez-Bermúdez ◽  
Manuel Fernández-Martínez
Keyword(s):  
Time Series ◽  
State Of The Art ◽  
Self Similarity ◽  
High Quality ◽  
Detailed Review ◽  
Physiological Time ◽  
Wide Range ◽  
Fractal Patterns ◽  
Self Similar ◽  
And Performance

AbstractAlong this paper, we shall update the state-of-the-art concerning the application of fractal-based techniques to test for fractal patterns in physiological time series. As such, the first half of the present work deals with some selected approaches to deal with the calculation of the self-similarity exponent of time series. They include broadly-used procedures as well as recent advances improving their accuracy and performance for a wide range of self-similar processes. The second part of this paper consists of a detailed review of high-quality studies carried out in the context of electroencephalogram signals. Both medical and non-medical applications have been deeply reviewed. This work is especially recommended to all those researchers especially interested in fractal pattern recognition for physiological time series.

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