The MDF technique for the analysis of tokamak edge plasma fluctuations

Tokamak edge plasma was analyzed by applying the multifractal detrend fluctuation analysis (MF-DFA) technique. This method has found wide application in the analysis of correlations and characterization of scaling behavior of the time-series data in physiology, finance, and natural sciences. The time evolution of the ion saturation current (Is), the floating potential fluctuation (Vf), the poloidal electric field (Ep), and the radial particle flux (Γr) has been measured by using a set of Langmuir probes consisting of four tips on the probe head. The generalized Hurst exponents (h(q)), local fluctuation function (Fq(s)), the Rényi exponents (τ(q)) as well as the multifractal spectrum f(αh) have been calculated by applying the MF-DFA method to Is, Vf, and the magnetohydrodynamic (MHD) fluctuation signal. Furthermore, we perform the shuffling and the phase randomization techniques to detect the sources of multifractality. The nonlinearity shape of τ(q) reveals a multifractal behavior of the time-series data. The results show that in the presence of biasing, Is, Vf, Ep, and Γr reduce about 25%, 90%, 70%, and 50%, respectively, compared with the situation with no biasing. Also, they reduce about 15%, 90%, 35%, and 25%, respectively, after resonant helical magnetic field (RHF) application. In the presence of biasing or RHF, the amplitude of the power spectrum of Is, Vf, Γr, and MHD activity reduce remarkably in all the ranges of frequency, while their h(q) increase. The values of h(q) have been restricted between 0.6 and 0.68. These results are evidence of the existence of long-range correlations in the plasma edge turbulence. They also show the self-similar nature of the plasma edge fluctuations. Biasing or RHF reduces the amount of Fq(s). The multifractal spectrum width of Is, Vf, and MHD fluctuation amplitude reduce about 60%, 70%, and 42%, respectively, by applying biasing. In the presence of RHF, their width reduces about 60%, 85%, and 75%, respectively. It means that biasing and RHF reduce the degree of multifractality.

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Long-Range Correlations and Characterization of Financial and Volcanic Time Series

Mathematics ◽

10.3390/math8030441 ◽

2020 ◽

Vol 8 (3) ◽

pp. 441 ◽

Cited By ~ 3

Author(s):

Maria C. Mariani ◽

Peter K. Asante ◽

Md Al Masum Bhuiyan ◽

Maria P. Beccar-Varela ◽

Sebastian Jaroszewicz ◽

...

Keyword(s):

Time Series ◽

Long Range ◽

Time Series Data ◽

Financial Time Series ◽

Seismic Station ◽

Volcanic Eruptions ◽

Series Data ◽

Fluctuation Analysis ◽

Scaling Properties ◽

Long Range Correlations

In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight.

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Modeling and forecasting multifractal wavelet scale: Western market versus eastern market

International Journal of Modern Physics C ◽

10.1142/s0129183118501097 ◽

2018 ◽

Vol 29 (11) ◽

pp. 1850109 ◽

Cited By ~ 1

Author(s):

Emrah Oral ◽

Gazanfer Unal

Keyword(s):

Time Series ◽

Time Series Data ◽

Moving Average ◽

Price Change ◽

Wavelet Coherence ◽

Series Data ◽

Primary Study ◽

Fluctuation Analysis ◽

Multifractal Detrended Fluctuation Analysis ◽

Time Frequency

This leading primary study is about modeling multifractal wavelet scale time series data using multiple wavelet coherence (MWC), continuous wavelet transform (CWT) and multifractal detrended fluctuation analysis (MFDFA) and forecasting with vector autoregressive fractionally integrated moving average (VARFIMA) model. The data is acquired from Yahoo Finances!, which is composed of 1671 daily stock market of eastern (NIKKEI, TAIEX, KOPSI) and western (SP500, FTSE, DAX) markets. Once the co-movement dependencies on time-frequency space are determined with MWC, the coherent data is extracted out of raw data at a certain scale by using CWT. The multifractal behavior of the extracted series is verified by MFDFA and its local Hurst exponents have been calculated obtaining root mean square of residuals at each scale. This inter-calculated fluctuation function time series has been re-scaled and used to estimate the process with VARFIMA model and forecasted accordingly. The results have shown that the direction of price change is determined without difficulty and the efficiency of forecasting has been substantially increased using highly correlated multifractal wavelet scale time series data.

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Fractal Complexity of Daily Physical Activity Patterns Differs With Age Over the Life Span and Is Associated With Mortality in Older Adults

The Journals of Gerontology Series A ◽

10.1093/gerona/gly247 ◽

2018 ◽

Vol 74 (9) ◽

pp. 1461-1467 ◽

Cited By ~ 3

Author(s):

David A Raichlen ◽

Yann C Klimentidis ◽

Chiu-Hsieh Hsu ◽

Gene E Alexander

Keyword(s):

Physical Activity ◽

Older Adults ◽

Time Series ◽

Time Scales ◽

Mortality Risk ◽

Time Series Data ◽

Series Data ◽

Fluctuation Analysis ◽

Wide Range ◽

Wearable Accelerometers

Abstract Background Accelerometers are included in a wide range of devices that monitor and track physical activity for health-related applications. However, the clinical utility of the information embedded in their rich time-series data has been greatly understudied and has yet to be fully realized. Here, we examine the potential for fractal complexity of actigraphy data to serve as a clinical biomarker for mortality risk. Methods We use detrended fluctuation analysis (DFA) to analyze actigraphy data from the National Health and Nutrition Examination Survey (NHANES; n = 11,694). The DFA method measures fractal complexity (signal self-affinity across time-scales) as correlations between the amplitude of signal fluctuations in time-series data across a range of time-scales. The slope, α, relating the fluctuation amplitudes to the time-scales over which they were measured describes the complexity of the signal. Results Fractal complexity of physical activity (α) decreased significantly with age (p = 1.29E−6) and was lower in women compared with men (p = 1.79E−4). Higher levels of moderate-to-vigorous physical activity in older adults and in women were associated with greater fractal complexity. In adults aged 50–79 years, lower fractal complexity of activity (α) was associated with greater mortality (hazard ratio = 0.64; 95% confidence interval = 0.49–0.82) after adjusting for age, exercise engagement, chronic diseases, and other covariates associated with mortality. Conclusions Wearable accelerometers can provide a noninvasive biomarker of physiological aging and mortality risk after adjusting for other factors strongly associated with mortality. Thus, this fractal analysis of accelerometer signals provides a novel clinical application for wearable accelerometers, advancing efforts for remote monitoring of physiological health by clinicians.

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DETRENDED FLUCTUATION ANALYSIS OF THE TCP-RED ALGORITHM

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409025328 ◽

2009 ◽

Vol 19 (12) ◽

pp. 4237-4245 ◽

Cited By ~ 1

Author(s):

XI CHEN ◽

SIU-CHUNG WONG ◽

CHI K. TSE ◽

LJILJANA TRAJKOVIĆ

Keyword(s):

Time Series ◽

Long Range ◽

Power Law ◽

Detrended Fluctuation Analysis ◽

Time Series Data ◽

Analytical Models ◽

Series Data ◽

Fluctuation Analysis ◽

Scaling Exponent ◽

Detrended Fluctuation

It has been observed that Internet gateways employing Transport Control Protocol (TCP) and the Random Early Detection (RED) control algorithm may exhibit instability and oscillatory behavior. Most control methods proposed in the past have been based on analytical models that rely on statistical measurements of network parameters. In this paper, we apply the detrended fluctuation analysis (DFA) method to analyze stability of the TCP-RED system. The DFA is used to analyze time-series data and generate power-law scaling exponents, which indicate the long-range correlations of the time series. We quantify the stability of the TCP-RED system by examining the variation of the DFA power-law scaling exponent when the system parameters are varied. We also study the long-range power-law correlations of TCP window periods.

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A Modified Multifractal Detrended Fluctuation Analysis (MFDFA) Approach for Multifractal Analysis of Precipitation in Dongting Lake Basin, China

Water ◽

10.3390/w11050891 ◽

2019 ◽

Vol 11 (5) ◽

pp. 891 ◽

Cited By ~ 7

Author(s):

Xike Zhang ◽

Gui Zhang ◽

Luo Qiu ◽

Bo Zhang ◽

Yurong Sun ◽

...

Keyword(s):

Time Series ◽

Time Series Data ◽

Daily Precipitation ◽

Dongting Lake ◽

Series Data ◽

Fluctuation Analysis ◽

Lake Basin ◽

Precipitation Time Series ◽

Multifractal Detrended Fluctuation Analysis ◽

Detrended Fluctuation

Multifractal detrended fluctuation analysis (MFDFA) method can examine higher-dimensional fractal and multifractal characteristics hidden in time series. However, removal of local trends in MFDFA is based on discontinuous polynomial fitting, resulting in pseudo-fluctuation errors. In this paper, we propose a two-stage modified MFDFA for multifractal analysis. First, an overlap moving window (OMW) algorithm is introduced to divide time series of the classic MFDFA method. Second, detrending by polynomial fitting local trend in traditional MFDFA is replaced by ensemble empirical mode decomposition (EEMD)-based local trends. The modified MFDFA is named OMW-EEMD-MFDFA. Then, the performance of the OMW-EEMD-MFDFA method is assessed by extensive numeric simulation experiments based on a p-model of multiplicative cascading process. The results show that the modified OMW-EEMD-MFDFA method performs better than conventional MFDFA and OMW-MFDFA methods. Lastly, the modified OMW-EEMD-MFDFA method is applied to explore multifractal characteristics and multifractal sources of daily precipitation time series data at the Mapoling and Zhijiang stations in Dongting Lake Basin. Our results showed that the scaling properties of the daily precipitation time series at the two stations presented a long-range correlation, showing a long-term persistence of the previous state. The strong q-dependence of H ( q ) and τ ( q ) indicated strong multifractal characteristics in daily precipitation time series data at the two stations. Positive Δ f values demonstrate that precipitation may have a local increasing trend. Comparing the generalized Hurst exponent and the multifractal strength of the original precipitation time series data with its shuffled and surrogate time series data, we found that the multifractal characteristics of the daily precipitation time series data were caused by both long-range correlations between small and large fluctuations and broad probability density function, but the broad probability density function was dominant. This study may be of practical and scientific importance in regional precipitation forecasting, extreme precipitation regulation, and water resource management in Dongting Lake Basin.

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Long-range correlation and nonlinearity in geochemical time series of gas discharges from Mt. Etna, and changes with 2001 and 2002–2003 eruptions

Nonlinear Processes in Geophysics ◽

10.5194/npg-17-733-2010 ◽

2010 ◽

Vol 17 (6) ◽

pp. 733-751 ◽

Cited By ~ 6

Author(s):

A. Paonita

Keyword(s):

Time Series ◽

Long Range ◽

Time Series Data ◽

Flicker Noise ◽

Series Data ◽

Scaling Exponent ◽

Time Reversibility ◽

Long Range Correlations ◽

Range Correlation ◽

Mt Etna

Abstract. In this paper, spectral and detrended fluctuation analyses, as well as time reversibility and magnitude-sign decomposition, have been applied to the 10-year time-series data resulting from geochemical monitoring of gas emissions on the flanks of Mt. Etna, and gases from a CO2 exploitation well located tens of kilometers from the volcano. The analysis of the time series which showed main effects of fractionation between gases due to selective dissolution in aquifers (e.g., the CO2 concentration series), revealed the occurrence of random fluctuations in time, typical of systems where several processes combine linearly. In contrast, the series of He isotopic composition exhibited power-law behavior of the second-order fluctuation statistics, with values of the scaling exponent close to 0.9. When related to the spectral exponent, this value indicates that the isotopic series closely resemble fractal flicker-noise signals having persistent long-range correlations. The isotopic signals also displayed asymmetry under time reversal and long-range correlation of the associated magnitude series, therefore it was statistically proved the presence of nonlinearity. Both long-range correlation and nonlinearity in time series have been generally considered as distinctive features of dynamic systems where numerous processes interact by feedback mechanisms, in accordance with the paradigm of self-organized criticality (SOC). Thus, it is here proposed that the system that generated the isotope series worked under conditions of SOC. Since the fluctuations of the isotope series have been related to magma degassing, the previous results place constraints on the dynamics of such process, and suggest that nonequilibrium conditions must be dominant. It remains unclear whether the signature of SOC is directly due to volatile degassing from magma, or if it derives from the interaction between melt and the stress field, which certainly influences magma decompression. The strength of scaling appears to increase after 2002 (α values from 0.8 up to 1.2), focusing on transition of the Etnean system from typical SOC toward conditions of lower criticality. By comparing this transition with those of geophysical observables, it can be suggested that the drop in the rate of magma supply, subsequent to the paroxysms of 2001 and 2002–2003, was the main cause of the scaling change.

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Graphical Exploratory Data Analysis for Categorical Longitudinal and Time Series Data

PsycEXTRA Dataset ◽

10.1037/e634372013-001 ◽

2013 ◽

Author(s):

Stephen J. Tueller ◽

Richard A. Van Dorn ◽

Georgiy Bobashev ◽

Barry Eggleston

Keyword(s):

Time Series ◽

Data Analysis ◽

Exploratory Data Analysis ◽

Time Series Data ◽

Series Data ◽

Exploratory Data

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Faktor-Faktor Yang Mempengaruhi Nilai Tukar Dollar Amerika Serikat Terhadap Rupiah Tahun 2000–2013

Jurnal Riset Manajemen Sekolah Tinggi Ilmu Ekonomi Widya Wiwaha Program Magister Manajemen ◽

10.32477/jrm.v1i2.72 ◽

2017 ◽

Vol 1 (2) ◽

pp. 177-191

Author(s):

Rizki Rahma Kusumadewi ◽

Wahyu Widayat

Keyword(s):

Time Series ◽

Exchange Rate ◽

Money Supply ◽

Time Series Data ◽

The United States ◽

Economic Conditions ◽

Series Data ◽

Arch Model ◽

United States Dollar ◽

The Exchange Rate

Exchange rate is one tool to measure a country’s economic conditions. The growth of a stable currency value indicates that the country has a relatively good economic conditions or stable. This study has the purpose to analyze the factors that affect the exchange rate of the Indonesian Rupiah against the United States Dollar in the period of 2000-2013. The data used in this study is a secondary data which are time series data, made up of exports, imports, inflation, the BI rate, Gross Domestic Product (GDP), and the money supply (M1) in the quarter base, from first quarter on 2000 to fourth quarter on 2013. Regression model time series data used the ARCH-GARCH with ARCH model selection indicates that the variables that significantly influence the exchange rate are exports, inflation, the central bank rate and the money supply (M1). Whereas import and GDP did not give any influence.

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