Crossover from antipersistent to persistent behavior in time series possessing the generalyzed dynamic scaling law

Balankin, Alexander S.; Matamoros, Oswaldo Morales; Gálvez, M Ernesto; Pérez, Ana

doi:10.1103/physreve.69.036121

Cited by 18 publications

(28 citation statements)

References 31 publications

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“…40 A common property of natural dynamic systems is the Scaling Invariance, which means that the central moments of first, second, third, and fourth order remain asymptotically constant in space and time. This phenomenon, called auto-affinity, is manifested in the time series if they are represented, in the first instance, in time intervals with decreasing duration, and it is observed that their appearance was similar.…”

Section: Scaling Invariance Degreementioning

confidence: 99%

“…The study of the variables and the interactions of a dynamic system through time focuses on finding patterns, structures, critical points of stability or instability, as well as the initial conditions sensibility to change, to achieve a certain degree of control. 40 A common property of natural dynamic systems is the Scaling Invariance, which means that the central moments of first, second, third, and fourth order remain asymptotically constant in space and time. 41 Generally, every real complex system exhibits scale invariance, that is, its behavior does not change by the rescaling of the variables that govern its dynamics.…”

Section: Scaling Invariance Degreementioning

confidence: 99%

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Wind speed variability study based on the Hurst coefficient and fractal dimensional analysis

Cadenas

Campos–Amezcua

Rivera

et al. 2019

Energy Science & Engineering

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This paper presents a study of a wind speed time series from La Venta, Oaxaca, Mexico. The time series consists of anemometric measurements taken by the Federal Electricity Commission of Mexico throughout a little over 6 years. The study was conducted to calculate the Hurst correlation coefficient using: box counting, rescaled range, power spectrum, detrended fluctuation analysis, and multifractal detrended fluctuation analysis techniques. The main objective of this research is to know the correlation among wind speed data to obtain a better description of real conditions of the time series, which is not always available, and to define the structure of its behavior. In this way, more suitable wind speed prediction models can be achieved. Results obtained from techniques above were used to generate fractals time series for a typical month, using the Hurst coefficient and a self‐affine trace generator, which produces fractals time series whose probability distribution is always normal. These time series were compared against time series generated by using random numbers with Gaussian behavior and the characteristics of a typical month. Fractals time series highlight in the qualitative part regarding the modeling of wind speed variability and the descriptive statistics (average, standard deviation, and coefficient of variation), which is similar to the real series. Discordance tests were applied to the datasets to detect deviated values, and so ensure the normal behavior of the samples. These tests showed the existence of different populations with normal behavior in the samples that had bimodal characteristics. By separating the samples, it was possible to apply the self‐affine trace generator to each population found, to generate the fractal time series. An additional objective was to find the level of change in the structure of the original series concerning its statistical and fractal characteristics at different window widths of the time series (daily, monthly, seasonal, and annual) to identify either a specific tendency or dynamic behavior. The results showed a wind speed time series with a negative correlation (antipersistent), a high degree of scale invariance (homothetic), and a fractal dimension very close to 2, thus indicating that the time series is more irregular than a random process.

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Section: Scaling Invariance Degreementioning

confidence: 99%

Section: Scaling Invariance Degreementioning

confidence: 99%

Wind speed variability study based on the Hurst coefficient and fractal dimensional analysis

Cadenas

Campos–Amezcua

Rivera

et al. 2019

Energy Science & Engineering

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“…Many statistical properties of financial markets have already been explored, and have revealed striking similarities between price volatility dynamics and the kinetic roughening of growing interfaces ( Figure 5). Based on this fact, (Balankin et al, 2004) the general dynamic scaling approach has been used to study the scaling properties of crude oil market.…”

Section: Fractals In Sciencesmentioning

confidence: 99%

Fractal behaviour of complex systems

2010

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One of the most important properties of systems is complexity. In a simple way, we can define the complexity of a system in terms of the number of elements that it contains, the nature and number of interrelations and the number of levels of embeddedness. When a high level of complexity exists in a system, it is considered a complex system. Complex systems can be soft systems and hard systems. In hard systems, when their elements are interrelated in a non-linear way, they are considered complex systems when they contain a great number of elements interacting in a non-linear way. To try to understand the behaviour of this type of system diverse mathematical tools have been developed. A new scientific discipline with great impact in the analysis of the complex systems has been developed in recent years, called fractal analysis. The study of the complex systems in the framework of fractal theory has been recognized as a new scientific discipline, being sustained by advances that have been made in diverse fields ranging from physics to economics. In this paper the history and the basic concepts of the fractal analysis of complex systems are discussed briefly and an oil crude price volatility fractal analysis is provided.

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“…[5,16]. It was found that both time series behave randomly with exponentially decaying auto-correlation function, whereas their fluctuations exhibit long-range power-law correlations.…”

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confidence: 99%