U.S. Politics from a multifractal perspective

Schadner, Wolfgang

doi:10.1016/j.chaos.2021.111677

Cited by 6 publications

(5 citation statements)

References 89 publications

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“…The unemployment and inflation rate are important factors that affect social stability and economic development. The dynamical analysis of unemployment and inflation models can deeply understand the current economic state and propose reasonable policies [36][37][38]. The unemployment rate refers to the proportion of surplus labor force in the whole labor force.…”

Section: Nonlinear Economic Systemmentioning

confidence: 99%

Generation mechanisms of strange nonchaotic attractors and multistable dynamics in a class of nonlinear economic systems

Duan

et al. 2023

Nonlinear Dyn

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In this paper we study strange nonchaotic attractors (SNAs) and multistable dynamics in a class of nonlinear economic systems. For quasiperiodically forced case, the generation and evolution mechanisms of SNAs are discussed. The fractal, Heagy-Hammel, torus doubling, and intermittency routes to SNAs are identified. The Lyapunov exponent, phase sensitive function and power spectrum are used to characterize the dynamical and geometrical properties of SNAs. Moreover, when multistable phenomenon occur in the system, the boundaries of the basin of attraction may become intertwined, which leads to the economic unpredictability in the long run.

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Section: Nonlinear Economic Systemmentioning

confidence: 99%

Generation mechanisms of strange nonchaotic attractors and multistable dynamics in a class of nonlinear economic systems

Duan

et al. 2023

Nonlinear Dyn

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“…The MF-DFA method is commonly used to examine the efficiency of the markets [14][15][16]. As well, MF-DFA can realize the effective analysis of social phenomena and events [17,18]. In addition, MF-DFA has been widely used in other sequence processing [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

“…17 exhibit the fitting performance, the generalized Hurst exponent and the scaling exponent. In general, the distribution of the generalized Hurst exponent computed through the MF-LSSVM-DFA model is more compact than that calculated by the MF-DFA model.…”

mentioning

confidence: 99%

Modified MF-DFA Model Based on LSSVM Fitting

Wang,

Zhong,

Yue

et al. 2024

Fractal Fract

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This paper proposes a multifractal least squares support vector machine detrended fluctuation analysis (MF-LSSVM-DFA) model. The system is an extension of the traditional MF-DFA model. To address potential overfitting or underfitting caused by the fixed-order polynomial fitting in MF-DFA, LSSVM is employed as a superior alternative for fitting. This approach enhances model accuracy and adaptability, ensuring more reliable analysis results. We utilize the p model to construct a multiplicative cascade time series to evaluate the performance of MF-LSSVM-DFA, MF-DFA, and two other models that improve upon MF-DFA from recent studies. The results demonstrate that our proposed modified model yields generalized Hurst exponents h(q) and scaling exponents τ(q) that align more closely with the analytical solutions, indicating superior correction effectiveness. In addition, we explore the sensitivity of MF-LSSVM-DFA to the overlapping window size s. We find that the sensitivity of our proposed model is less than that of MF-DFA. We find that when s exceeds the limited range of the traditional MF-DFA, h(q) and τ(q) are closer than those obtained in MF-DFA when s is in a limited range. Meanwhile, we analyze the performances of the fitting of the two models and the results imply that MF-LSSVM-DFA achieves a better outstanding performance. In addition, we put the proposed MF-LSSVM-DFA into practice for applications in the medical field, and we found that MF-LSSVM-DFA improves the accuracy of ECG signal classification and the stability and robustness of the algorithm compared with MF-DFA. Finally, numerous image segmentation experiments are adopted to verify the effectiveness and robustness of our proposed method.

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“…The reason for this is that an uncertain system produces different measurements for each observation, and therefore one single system measurement is not representative of its behavior. Therefore, the application of MFDFA on a single time series obtained from an uncertain system cannot provide meaningful results and, unlike what is commonly done in the literature (e.g., [13][14][15][16]), a large number of signals must be considered in the analysis.…”

Section: Introductionmentioning

confidence: 99%

Multi-Signal Multifractal Detrended Fluctuation Analysis for Uncertain Systems —Application to the Energy Consumption of Software Programs in Microcontrollers

de la Torre,

Pavón-Domínguez,

Dorronsoro

et al. 2023

Fractal Fract

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Uncertain systems are those wherein some variability is observed, meaning that different observations of the system will produce different measurements. Studying such systems demands the use of statistical methods over multiple measurements, which allows overcoming the uncertainty, based on the premise that a single measurement is not representative of the system’s behavior. In such cases, the current multifractal detrended fluctuation analysis (MFDFA) method cannot offer confident conclusions. This work presents multi-signal MFDFA (MS-MFDFA), a novel methodology for accurately characterizing uncertain systems using the MFDFA algorithm, which enables overcoming the uncertainty of the system by simultaneously considering a large set of signals. As a case study, we consider the problem of characterizing software (Sw) consumption. The difficulty of the problem mainly comes from the complexity of the interactions between Sw and hardware (Hw), as well as from the high uncertainty level of the consumption measurements, which are affected by concurrent Sw services, the Hw, and external factors such as ambient temperature. We apply MS-MFDFA to generate a signature of the Sw consumption profile, regardless of the execution time, the consumption levels, and uncertainty. Multiple consumption signals (or time series) are built from different Sw runs, obtaining a high frequency sampling of the instant input current for each of them while running the Sw. A benchmark of eight Sw programs for analysis is also proposed. Moreover, a fully functional application to automatically perform MS-MFDFA analysis has been made freely available. The results showed that the proposed methodology is a suitable approximation for the multifractal analysis of a large number of time series obtained from uncertain systems. Moreover, analysis of the multifractal properties showed that this approach was able to differentiate between the eight Sw programs studied, showing differences in the temporal scaling range where multifractal behavior is found.

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U.S. Politics from a multifractal perspective

Cited by 6 publications

References 89 publications

Generation mechanisms of strange nonchaotic attractors and multistable dynamics in a class of nonlinear economic systems

Generation mechanisms of strange nonchaotic attractors and multistable dynamics in a class of nonlinear economic systems

Modified MF-DFA Model Based on LSSVM Fitting

Multi-Signal Multifractal Detrended Fluctuation Analysis for Uncertain Systems —Application to the Energy Consumption of Software Programs in Microcontrollers

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