Search

Every woman spends her life with a cyclic occurrence of the menstrual cycle of approximately 28 days. During a menstrual cycle, there are many physical, psychological and behavioural changes in women that affect the autonomic activities of the heart. However, health management is an important factor to be considered as it influences the entire quality of women life. Thus, Heart Rate Variability (HRV) analysis is an appropriate tool to examine the physiological effects of the menstrual cycle in young healthy women. So, in this paper, Detrended Fluctuation Analysis method (DFA) is used for analyzing the HRV in the phases of the menstrual cycle. In DFA, there is a limitation of abrupt jumps in detrended profile that leads to the inaccurate detection of properties of HRV. In order to overcome the limitations of abrupt jumps in the DFA method, a novel method is proposed in this paper. The trend in proposed method is created by averaging the integrated HRV time series of each window in its respective time scale. Then, cubic interpolation is done for estimating new data points within each averaged segment. Finally, proposed trend is used to estimate scaling exponent function. The proposed method detects the properties of HRV variations accurately among phases of the menstrual cycle when applied on self-recorded dataset.

The present study is designed to analyse the annual rainfall variability and trend in 30 meteorological stations of the Asir region for the period of 1970–2017 using the Mann-Kendall (MK) test, Modified Mann-Kendall (MMK) test, trend free pre-whitening Mann-Kendall (TFPW MK) test, and the innovative trend analysis (ITA). A comparative study among the trend detection techniques was performed using the correlation coefficient. The future rainfall trend based on the historical rainfall pattern was investigated by using detrended fluctuation analysis (DFA). Results of the MK test showed that 20 stations in the study area observed a negative trend, and out of these, nine stations had significant negative trends at the significance level of 0.01. The findings of the MMK test showed that 23 stations recorded negative trends, and out of these, 18 stations had significant negative trends at the significance level of 0.01. Based on the findings of the TFPW-MK test, 21 stations observed a negative trend, and among these, 10 stations had significant negative trends at the significance of 0.01. ITA detected 25 stations observing a negative trend, and out of these, 18 stations had significant negative trends at the significance level of 0.01. Based on the findings of the tests and their performance, the MMK test appeared as the best performing technique among the MK test family, while ITA appeared as the best trend detection technique among the four techniques because it outperformed (p

Control system performance assessment is significant, especially in practical applications. One of the most important indices for the performance assessment of control systems is minimum variance. Calculating the minimum variance index in multivariate systems requires prior knowledge of system parameters and models, and is therefore an obstacle in practical applications. In this article, an index is proposed for the performance assessment of multivariate control loops, evaluating the system performance with the minimum variance criterion and using only the system’s routine operation data. This index can quantify the performance using neither any prior knowledge of system parameters nor the system’s optimal operation data. The proposed index is based on the Hurst exponent, a parameter for measuring correlations in time series data. In this article, detrended fluctuation analysis and rescaled range analysis are used to estimate the Hurst exponents of system outputs. Using a combination of these Hurst exponents, an index is defined for the performance assessment of multivariate systems. The results of simulation examples illustrate that the proposed index can assess the performance efficiently.

This study analysed long-term rainfall data (1851–2006) over seven climatic zones of India at seasonal and annual scales based on three techniques: (i) linear regression, (ii) multifractal detrende...

In this study, an attempt has been made to analyze uterine Electromyography (uEMG) signals during Term conditions (pregnancy duration more than 37 weeks of gestational age) using Empirical Mode Decomposition based Detrended Fluctuation Analysis (EMD-DFA). The Term delivery signals are considered from a publicly available database, grouped as T1 (

The present study examined how prevalent methods for determining maximal voluntary contraction (MVC) impact the experimentally derived functions of graded force-force variability. Thirty-two young healthy subjects performed continuous isometric force tracking (20 s trials) at 10 target percentages (5–95% MVC) normalized to a conventional discrete-point (n = 16), or sustained (n = 16) MVC calculation. Distinct rates and magnitudes of change were observed for absolute variability (standard deviation (SD), root mean squared error (RMSE)), tracking error (RMSE, constant error (CE)), and complexity (detrended fluctuation analysis (DFA)) (all p &lt, 0.05) of graded force fluctuations between the MVC groups. Differential performance strategies were observed beyond ~65% MVC, with the discrete-point group minimizing their SD at force values below that of the criterion target (higher CE/RMSE). Moreover, the sustained group’s capacity to minimize SD/RMSE/CE corresponded to a more complex structure in their force fluctuations. These findings reveal that the time component of MVC estimation has a direct influence on the corrective strategies supporting near-maximal manual force control. While discrete MVC protocols predominate in the study of manual strength/endurance/precision, a 1:1 MVC-task mapping appears more to be ecologically valid if visuo-motor precision outcomes are of central importance.

The influence of reduction in emissions on the inherent temporal characteristics of PM2.5 and NO2 concentration time series in six urban cities of India is assessed by computing the Hurst exponent using Detrended Fluctuation Analysis (DFA) during the lockdown period (March 24–April 20, 2020) and the corresponding period during the previous two years (i.e., 2018 and 2019). The analysis suggests the anticipated impact of confinement on the PM2.5 and NO2 concentration in urban cities, causing low concentrations. It is observed that the original PM2.5 and NO2 concentration time series is persistent but filtering the time series by fitting the autoregressive process of order 1 on the actual time series and subtracting it changes the persistence property significantly. It indicates the presence of linear correlations in the PM2.5 and NO2 concentrations. Hurst exponent of the PM2.5 and NO2 concentration during the lockdown period and previous two years shows that the inherent temporal characteristics of the short-term air pollutant concentrations (APCs) time series do not change even after withholding the emissions. The meteorological variations also do not change over the three time periods. The finding helps in developing the prediction models for future policy decisions to improve urban air quality across cities.

The anomalous diffusive processes are widely discussed in the research papers. In contrast to the diffusive processes with the linear second moment, they are characterized by the nonlinear variance. The anomalous diffusive processes exhibit many interesting properties which are not adequate to the diffusive systems and thus they have found various applications including, among others, biology, physics and environmental engineering. Very useful in the testing of the anomalous diffusive behavior are the time-averaged statistics which are based on the sample trajectory of the given process. Similar as the empirical second moment, they exhibit different behavior for anomalous diffusive and diffusive processes. Thus, they can be very effective tools for the estimation and statistical testing of the anomalous diffusive behavior. One can find different theoretical anomalous diffusive processes. One of the classical examples is the fractional Brownian motion. In this chapter, we demonstrate how the selected time-averaged statistics behave for the fractional Brownian motion and show how they can be applied in order to estimate the Hurst exponent (responsible for the anomalous diffusive behavior). By using Monte Carlo simulations, we compare the effectiveness of the presented estimation methods for the considered stochastic process. The described methodology can be applied to any other anomalous diffusive processes.

Satellite-derived Normalized Difference Vegetation index (NDVI) data records offer important sources for long term correlation modelling over West Africa. In this study, we assessed long range correlations in half monthly NDVI records over West Africa from 1982 to 2011 using GIMMS NDVI. In our analysis, we assessed (a) the annual and seasonal trends obtained using Ordinary Linear Regression, (b) the detrended lag-1-autocorrelation C(1), (c) the Detrended Fluctuation Analysis (DFA) scaling Hurst exponent h and (d) the Multifractal (MF) characteristics of NDVI. Results show that there exist some patterns or trends in the records that persist over time. The value of C(1) for NDVI was obtained as 0.989 is significant at 95% confidence interval. Consequently, the scaling h values of the Hurst DFA showed that about 37.4, 20.5, 41.7 and 0.5% of the vegetated areas are anti-correlated (h

Recent study points to the value of a non-linear heart rate variability (HRV) biomarker using detrended fluctuation analysis (DFA a1) for aerobic threshold determination (HRVT). Significance of recording artefact, correction methods and device bias on DFA a1 during exercise and HRVT is unclear. Gas exchange and HRV data were obtained from 17 participants during an incremental treadmill run using both ECG and Polar H7 as recording devices. First, artefacts were randomly placed in the ECG time series to equal 1, 3 and 6% missed beats with correction by Kubios software&rsquo, s automatic and medium threshold method. Based on linear regression, Bland Altman analysis and Wilcoxon paired testing, there was bias present with increasing artefact quantity. Regardless of artefact correction method, 1 to 3% missed beat artefact introduced small but discernible bias in raw DFA a1 measurements. At 6% artefact using medium correction, proportional bias was found (maximum 19%). Despite this bias, the mean HRVT determination was within 1 bpm across all artefact levels and correction modalities. Second, the HRVT ascertained from synchronous ECG vs. Polar H7 recordings did show an average bias of minus 4 bpm. Polar H7 results suggest that device related bias is possible but in the reverse direction as artefact related bias.

Forecasting the particulate matter (PM) concentration in South Korea has become urgently necessary owing to its strong negative impact on human life. In most statistical or machine learning methods, independent and identically distributed data, for example, a Gaussian distribution, are assumed; however, time series such as air pollution and weather data do not meet this assumption. In this study, the maximum correntropy criterion for regression (MCCR) loss is used in an analysis of the statistical characteristics of air pollution and weather data. Rigorous seasonality adjustment of the air pollution and weather data was performed because of their complex seasonality patterns and the heavy-tailed distribution of data even after deseasonalization. The MCCR loss was applied to multiple models including conventional statistical models and state-of-the-art machine learning models. The results show that the MCCR loss is more appropriate than the conventional mean squared error loss for forecasting extreme values., Comment: J Mech Sci Technol 35 4045-4063 (2021)

The short-term scaling exponent alpha1 of detrended fluctuation analysis (DFA a1), a nonlinear index of heart rate variability (HRV) based on fractal correlation properties, has been shown to steadily change with increasing exercise intensity. To date, no study has specifically examined using the behavior of this index as a method for defining a low intensity exercise zone. The aim of this report is to compare both oxygen intake (VO2) and heart rate (HR) reached at the first ventilatory threshold (VT1), a well-established delimiter of low intensity exercise, to those derived from a predefined DFA a1 transitional value. Gas exchange and HRV data were obtained from 15 participants during an incremental treadmill run. Comparison of both VO2 and HR reached at VT1 defined by gas exchange (VT1 GAS) was made to those parameters derived from analysis of DFA a1 reaching a value of 0.75 (HRVT). Based on Bland Altman analysis, linear regression, intraclass correlation (ICC) and t testing, there was strong agreement between VT1 GAS and HRVT as measured by both HR and VO2. Mean VT1 GAS was reached at 39.8 ml/kg/min with a HR of 152 bpm compared to mean HRVT which was reached at 40.1 ml/kg/min with a HR of 154 bpm. Strong linear relationships were seen between test modalities, with Pearson’s r values of 0.99 (p < 0.001) and.97 (p < 0.001) for VO2 and HR comparisons, respectively. Intraclass correlation between VT1 GAS and HRVT was 0.99 for VO2 and 0.96 for HR. In addition, comparison of VT1 GAS and HRVT showed no differences by t testing, also supporting the method validity. In conclusion, it appears that reaching a DFA a1 value of 0.75 on an incremental treadmill test is closely associated with crossing the first ventilatory threshold. As training intensity below the first ventilatory threshold is felt to have great importance for endurance sport, utilization of DFA a1 activity may provide guidance for a valid low training zone.

Accelerometry data has been widely used to measure activity and the circadian rhythm of individuals across the health sciences, in particular with people with advanced dementia. Modern accelerometers can record continuous observations on a single individual for several days at a sampling frequency of the order of one hertz. Such rich and lengthy data sets provide new opportunities for statistical insight, but also pose challenges in selecting from a wide range of possible summary statistics, and how the calculation of such statistics should be optimally tuned and implemented. In this paper, we build on existing approaches, as well as propose new summary statistics, and detail how these should be implemented with high frequency accelerometry data. We test and validate our methods on an observed data set from 26 recordings from individuals with advanced dementia and 14 recordings from individuals without dementia. We study four metrics: Interdaily stability (IS), intradaily variability (IV), the scaling exponent from detrended fluctuation analysis (DFA), and a novel nonparametric estimator which we call the proportion of variance (PoV), which calculates the strength of the circadian rhythm using spectral density estimation. We perform a detailed analysis indicating how the time series should be optimally subsampled to calculate IV, and recommend a subsampling rate of approximately 5 minutes for the dataset that has been studied. In addition, we propose the use of the DFA scaling exponent separately for daytime and nighttime, to further separate effects between individuals. We compare the relationships between all these methods and show that they effectively capture different features of the time series.

This work presents an analysis of low-visibility event persistence and prediction at Villanubla Airport (Valladolid, Spain), considering Runway Visual Range (RVR) time series in winter. The analysis covers long- and short-term persistence and prediction of the series, with different approaches. In the case of long-term analysis, a Detrended Fluctuation Analysis (DFA) approach is applied in order to estimate large-scale RVR time series similarities. The short-term persistence analysis of low-visibility events is evaluated by means of a Markov chain analysis of the binary time series associated with low-visibility events. We finally discuss an hourly short-term prediction of low-visibility events, using different approaches, some of them coming from the persistence analysis through Markov chain models, and others based on Machine Learning (ML) techniques. We show that a Mixture of Experts approach involving persistence-based methods and Machine Learning techniques provides the best results in this prediction problem.

Objective: U-shaped patterns, characteristic periods of time observed in tachograms, are a specific subgroup among very low frequency components characterized by relatively short periods of smooth accelerations followed by decelerations of heart rhythm. In this study, we characterize this phenomenon and its effect on heart rate variability (HRV) parameters. Approach: We calculated linear (the mean and standard deviation of RR intervals, RMSSD, pNN50 and the power of the frequency components) and nonlinear (V0, V1 and V2 Porta’s symbolic analysis, Shannon and Sample entropy, Guzik’s and Porta’s asymmetry indexes, the exponents α1 and α2 of detrended fluctuation analysis and the Hurst surface h(q,s) of multiscale multifractal analysis (MMA)) HRV parameters for 65 RR interval night-time series (39 females, 37.5(11.3) years old and 26 males, 41.7(16.5) years old; all without organic heart diseases). All parameters were calculated for original data and for the three kinds of test data in which the following parts of the time series were replaced by 1/f noise: (A) the U-shape patterns annotated in a given data set, (B) randomly chosen windows of similar size as the U-shaped patterns, (C) acceleration-deceleration events shorter than U-shaped patterns. Main results: We found that the U-shaped patterns, as the most persistent structures in RR night-time intervals series, affect the long-range correlation properties (measured by α2). We also found that the U-shaped patterns importantly strictly affect the shape of h(q,s) surface at different scales s. Removing the U-shaped patterns results in the shape of the h(q,s) surface losing the properties characteristic for healthy heart rhythm. The largest quantitative effect of U-shaped patterns was obtained for the power of the VLF component. The mean percentage difference of the VLF component between the original data and the A to C type test data were 19.4%, −4.3% and 5.3%, respectively. Significance: Although percentage contribution of U-shaped patterns is small compared to the whole night-time series (on the average 3.1%(1.7%) with a standard deviation of 1.7%), these patterns have a considerable impact on the HRV parameters describing the VLF, persistency, nonlinear correlations and multifractal properties.

Introduction: Heart rate variability (HRV) can be assessed from RR-intervals. These are derived from an electrocardiographic PQRST-signature and can deviate in a chaotic or irregular manner. In the past, techniques from statistical physics have allowed researchers to study such systems. Objective: This study planned to assess the heart rate dynamics in young obese subjects by nonlinear metrics to heart rate variability. Methods: 86 subjects were split equally according to status. Heart rate was recorded with the subjects resting in a dorsal (prone) position for 30 minutes. The complexity of the RR-intervals was assessed by five Entropies, Detrended Fluctuation Analysis, Higuchi and Katz’s fractal dimensions Following inconclusive tests of normality we calculated the One-Way Analysis of Variance, Kruskal-Wallis, and the Effect Sizes by Cohen’s d significances. Results: It was established that Shannon, Renyi and Tsallis Entropies and the Higuchi and Katz・s fractal dimensions could significantly discriminate the two groups. The three entropies were higher in obese youths, suggesting less predictable sets of RR intervals (p

This study empirically compares the development of China’s interest rate market in the past decade. The yield of Shibor market from 2006 to 2016 showed anti-persistence, and the later five-year trend was stronger than that in the previous half period, indicating a significantly growing trend of China’s interest rate market. We perform a comparative analysis of detrended fluctuation analysis (DFA), detrending moving average (DMA) algorithm, and the maximum overlap wavelet transform (DFA-MODWT) using grey and original sequences. The autoregressive integrated moving average model is adopted to generate set-point H sequences. Results illustrated that 1) for original sequences, both the DFA-MODWT and DMA ( θ = 0 . 5 ) shows outstanding performances when the set Hurst exponents are 0.6 and 0.7 and 0.8 and 0.9, respectively. 2) For grey sequences, G-DFA performs best among the three methods, followed by G-DMA and G-DFA-MODWT. 3) The long-range correlation of the original sequences is slightly lower than the set values. On the contrary, the long-range correlation of grey sequences is much higher than the set values. Thus, the grey sequence exerts a strong aggregation effect as it can accumulate the trend of the sequence. Our results show that the grey sequence can determine the regular pattern from the messy sequence. However, grey sequences tend to be overly analyzed and misleading when large volumes of data are involved. Empirical studies confirm that China’s interest rate market remains an inefficient market.

Heart rate asymmetry is a phenomenon by which the accelerations and decelerations of heart rate behave differently, and this difference is consistent and unidirectional, i.e. in most of the analyzed recordings the inequalities have the same directions. So far, it has been established for variance and runs based types of descriptors of R R intervals time series. In this paper we apply the newly developed method of Asymmetric Detrended Fluctuation Analysis, which so far has mainly been used with economic time series, to the set of 420 stationary 30 min time series of R R intervals from young, healthy individuals aged between 20 and 40. This asymmetric approach introduces separate scaling exponents for rising and falling trends. We systematically study the presence of asymmetry in both global and local versions of this method. In this study global means “applying to the whole time series” and local means “applying to windows jumping along the recording”. It is found that the correlation structure of the fluctuations left over after detrending in physiological time series shows strong asymmetric features in both magnitude, with α + α − , where α + is related to heart rate decelerations and α − to heart rate accelerations, and the proportion of the signal in which the above inequality holds. A very similar effect is observed if asymmetric noise is added to a symmetric self-affine function. No such phenomena are observed in the same physiological data after shuffling or with a group of symmetric synthetic time series.

Detrended Fluctuation Analysis (DFA) has become a widely-used tool to examine the correlation structure of a time series and provided insights into neuromuscular health and disease states. As the popularity of utilizing DFA in the human behavioral sciences has grown, understanding its limitations and how to properly determine parameters is becoming increasingly important. DFA examines the correlation structure of variability in a time series by computing α , the slope of the log S D – log n diffusion plot. When using the traditional DFA algorithm, the timescales, n , are often selected as a set of integers between a minimum and maximum length based on the number of data points in the time series. This produces non-uniformly distributed values of n in logarithmic scale, which influences the estimation of α due to a disproportionate weighting of the long-timescale regions of the diffusion plot. Recently, the evenly spaced DFA and evenly spaced average DFA algorithms were introduced. Both algorithms compute α by selecting k points for the diffusion plot based on the minimum and maximum timescales of interest and improve the consistency of α estimates for simulated fractional Gaussian noise and fractional Brownian motion time series. Two issues that remain unaddressed are (1) how to select k and (2) whether the evenly-spaced DFA algorithms show similar benefits when assessing human behavioral data. We manipulated k and examined its effects on the accuracy, consistency, and confidence limits of α in simulated and experimental time series. We demonstrate that the accuracy and consistency of α are relatively unaffected by the selection of k . However, the confidence limits of α narrow as k increases, dramatically reducing measurement uncertainty for single trials. We provide guidelines for selecting k and discuss potential uses of the evenly spaced DFA algorithms when assessing human behavioral data.

In this paper, a generalized method of detrended fluctuation analysis (DFA) is proposed as a new measure to assess the complexity of a complex dynamical system such as stock market. We extend DFA and local scaling DFA to higher moments such as skewness and kurtosis (labeled SMDFA and KMDFA), so as to investigate the volatility scaling property of financial time series. Simulations are conducted over synthetic and financial data for providing the comparative study. We further report the results of volatility behaviors in three American countries, three Chinese and three European stock markets by using DFA and LSDFA method based on higher moments. They demonstrate the dynamics behaviors of time series in different aspects, which can quantify the changes of complexity for stock market data and provide us with more meaningful information than single exponent. And the results reveal some higher moments volatility and higher moments multiscale volatility details that cannot be obtained using the traditional DFA method.

Nas últimas décadas o comércio de frutas no Brasil cresceu expressivamente atendendo ao mercado interno e externo. Dentre as principais frutas produzidas e comercializadas, destaca-se a manga, a fruta mais exportada pelo Brasil. Neste trabalho foram analisadas as séries temporais de retornos e de volatilidade de preços semanais de duas variedades de manga, Palmer e Tommy Atkins, produzidas no Vale do São Francisco, a região com a maior produção de manga no país. Foram utilizados os métodos Detrended Fluctuation Analysis (DFA) e Detrended Cross-Correlation Analysis (DCCA) para calcular expoentes de escala de autocorrelações e correlações cruzadas entre as séries analisadas. Os resultados mostraram que as séries de volatilidade apresentam persistência mais forte do que as séries de retornos que apresentaram dois regimes de invariância de escala com correlações antipersistentes nas escalas maiores. As correlações cruzadas entre as séries de retornos também apresentaram dois regimes de escala com expoentes semelhantes as séries de retornos da variedade Tommy. Os valores do coeficiente de correlação obtidos pelo método Detrended Cross Correlation Coefficient mostraram que para ambas, retornos e volatilidade, as correlações entre as séries são positivas, aumentam com escala temporal e são mais fortes para as séries de retornos.

Climate change is deeply impacting the society on different scales. Decision making becomes a complex task when, in adverse weather conditions, the meteorological records show missing data due to failures of measuring instruments. Several investigations have proposed optimized regression methods, K-nearest-neighbor imputation, and multiple imputations for the treatment of missing data; however, there is less information about the application of imputation methods for the treatment of missing data on short meteorological records. Therefore, the expected confidence in the results requires using robust analysis methods that depend the least as possible on the length of the records and the number of missing data. In this research, the performance of detrended fluctuation analysis applied on temperature short record was studied when K-nearest-neighbor and neural networks are used as imputation techniques, and compared with the performance without data imputation. The results showed the robustness when it is applied to a short time series with missing data and without data imputation. In this aspect, the DFA method only requires removing the seasonality from the temperature records to get good performance.

In this paper, we analyzed price–volume multifractal cross-correlations of Moroccan Stock Exchange. We chose the period from January 1st 2000 to January 20th 2017 to investigate the multifractal behavior of price change and volume change series. Then, we used multifractal detrended cross-correlations analysis method (MF-DCCA) and multifractal detrended fluctuation analysis (MF-DFA) to analyze the series. We computed bivariate generalized Hurst exponent, Renyi exponent and spectrum of singularity for each pair of indices to measure quantitatively cross-correlations. Furthermore, we used detrended cross-correlations coefficient (DCCA) and cross-correlation test ( Q ( m ) ) to analyze cross-correlation quantitatively and qualitatively. By analyzing results, we found existence of price–volume multifractal cross-correlations. The spectrum width has a strong multifractal cross-correlation. We remarked that volume change series is anti-persistent when we analyzed the generalized Hurst exponent for all moments q . The cross-correlation test showed the presence of a significant cross-correlation. However, DCCA coefficient had a small positive value, which means that the level of correlation is not very significant. Finally, we analyzed sources of multifractality and their degree of contribution in the series.

This study aimed to analyze the time series behavior of the Southern Oscillation Index through techniques using Fast Fourier Transform, computing the autocorrelation function, and the calculation of the Hurst coefficient. The methodology of Hurst Exponent calculation uses different lags, which are computed in the time series of Southern Oscillation Index. The persistent behavior in the time series can be characterized by calculating the Hurst Exponent, seeking for more behavioral information, as the existence of persistence and/or terms of long-range memory in the series. The results show a persistence of the climate in terms of long-memory Southern Oscillation Index time series, which can help to understand a complex dynamic behavior in climate effects at global-scale level and specifically its influence in northeastern Brazil, in the region of the Alcântara Launch Center. The R package tseriesChaos was used in the analysis of the Southern Oscillation Index time series, estimating the largest Lyapunov exponent, which indicates the existence of chaotic behavior in time series. The resampling technique was used in a permutation test between the surface wind data in the São Luís airport, Maranhão State, and the Southern Oscillation Index. The permutation test results showed that the time series of monthly average wind speed in the São Luís airport is correlated with the variability of Southern Oscillation Index, statistically correlated to the confidence interval at the 5% level. The results showed the possibility of using autoregressive models to represent average variable meteorology in the behavior analysis as well as trends in the climate, more specifically a possible climatic influence of El Niño-Southern Oscillation in wind strength in the Alcântara Launch Center.

Long-range autocorrelations (LRA) are a robust feature of rhythmic movements, which may provide important information about neural control and potentially constitute a powerful marker of dysfunction. A clear difficulty associated with the assessment of LRA is that it requires a large number of cycles to generate reliable results. Here we investigate how series length impacts the reliability of LRA assessment. A total of 94 time series extracted from walking or cycling tasks were re-assessed with series length varying from 64 to 512 data points. LRA were assessed using an approach combining the rescaled range analysis or the detrended fluctuation analysis (Hurst exponent, H), along with the shape of the power spectral density (α exponent). The statistical precision was defined as the ability to obtain estimates for H and α that are consistent with their theoretical relationship, irrespective of the series length. The sensitivity consisted of testing whether significant differences between experimental conditions found in the original studies when considering 512 data points persisted with shorter series. We also investigate the use of evenly-spaced diffusion plots as a methodological improvement of original version of methods for short series. Our results show that the reliable assessment of LRA requires 512 data points, or no shorter than 256 data points provided that more robust methods are considered such as the evenly-spaced algorithms. Such series can be reasonably obtained in clinical populations with moderate, or even more severe, gait impairments and open the perspective to extend the use of LRA assessment as a marker of gait stability applicable to a broad range of locomotor disorders.

Stride-to-stride time intervals during human walking are characterised by predictability and statistical persistence quantified by sample entropy (SaEn) and detrended fluctuation analysis (DFA) which indicates a time dependency in the gait pattern. However, neither analyses quantify time dependency in a physical or physiological interpretable time scale. Recently, entropic half-life (ENT½) has been introduced as a measure of the time dependency on an interpretable time scale. A novel measure of time dependency, based on DFA, statistical persistence decay (SPD), was introduced. The present study applied SaEn, DFA, ENT½, and SPD in known theoretical signals (periodic, chaotic, and random) and stride-to-stride time intervals during overground and treadmill walking in healthy subjects. The analyses confirmed known properties of the theoretical signals. There was a significant lower predictability (p = 0.033) and lower statistical persistence (p = 0.012) during treadmill walking compared to overground walking. No significant difference was observed for ENT½ and SPD between walking condition, and they exhibited a low correlation. ENT½ showed that predictability in stride time intervals was halved after 11-14 strides and SPD indicated that the statistical persistency was deteriorated to uncorrelated noise after ~50 strides. This indicated a substantial time memory, where information from previous strides affected the future strides.

A set of methods for the pre-forecasting fractal time series analysis to determine the levels of persistence of chaotic information flows in the well-drilling control system is proposed. Based on this methodology, the values of the Hurst exponent H, fractal dimension D, spatial dimension n and correlation measure C are obtained for six time series. Since the Hurst exponent H for all the signals is greater than 0.5, the conclusion about a chaotic nature of the studied time series is made. However, the dynamics of these signals will not change and it can be predicted that it will evolve in the same direction as in the past. This allows using the obtained results for forecasting and early detection of deviations of the drilling process from the norm. Since the oil and gas well drilling process is a complex stochastic process proceeding in conditions of a priori and current uncertainty under the influence of immeasurable disturbances, calculation of the Hurst exponent H contributes to solving the forecasting problems in the automated support system of decision-making regarding well-drilling process control

Variability of oxyhemoglobin saturation during sleep has been utilized as diagnostic index for sleep apnea. This work examined the parameters of a detrended fluctuation analysis (DFA) plot created from series data for oxyhemoglobin saturation during a sleep study in 273 subjects. A novel automated algorithm was devised to measure the parameters of a DFA log–log plot that included the slopes of 4 line segments and the coordinates and angles of their intersections. The diagnostic value of the parameters was investigated by receiver operating characteristic (ROC) curves using apnea/hypopnea index (AHI) cutoff values of 5, 15, and 30. Three of the DFA plot parameters exhibited an area under the ROC curve ≥0.89 for all three AHI cutoff values. Principal component analysis found a surrogate variable that increased the areas under ROC curves to greater than 0.92 for all of the AHI cutoff values. The algorithm was “leave-one-out” cross-validated and validated in another 206 subjects receiving polysomnographic studies. The results demonstrate that the DFA plot of oxyhemoglobin saturation is a useful tool for screening subjects with sleep apnea.

Purpose The Hurst exponent has been very important in telling the difference between fractal signals and explaining their significance. For estimators of the Hurst exponent, accuracy and efficiency are two inevitable considerations. The main purpose of this study is to raise the execution efficiency of the existing estimators, especially the fast maximum likelihood estimator (MLE), which has optimal accuracy. Design/methodology/approach A two-stage procedure combining a quicker method and a more accurate one to estimate the Hurst exponent from a large to small range will be developed. For the best possible accuracy, the data-induction method is currently ideal for the first-stage estimator and the fast MLE is the best candidate for the second-stage estimator. Findings For signals modeled as discrete-time fractional Gaussian noise, the proposed two-stage estimator can save up to 41.18 per cent the computational time of the fast MLE while remaining almost as accurate as the fast MLE, and even for signals modeled as discrete-time fractional Brownian motion, it can also save about 35.29 per cent except for smaller data sizes. Originality/value The proposed two-stage estimation procedure is a novel idea. It can be expected that other fields of parameter estimation can apply the concept of the two-stage estimation procedure to raise computational performance while remaining almost as accurate as the more accurate of two estimators.

There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. This paper presents two-dimensional multifractal cross-correlation analysis based on the partition function (2D-MFXPF), two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) and two-dimensional multifractal cross-correlation analysis based on the detrended moving average analysis (2D-MFXDMA). We apply these methods to pairs of two-dimensional multiplicative cascades (2D-MC) to do a comparative study. Then, we apply the two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) to real images and unveil intriguing multifractality in the cross correlations of the material structures. At last, we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms in the potential applications in the field of SAR image classification and detection.

The primary purpose of this study was to find Bayesian estimates for the Hurst dimension of a Fractional Brownian motion with a Beta prior when the process is observed at discrete times. Overestimation is observed though the overestimation is less severe as real H goes up. In addition, the estimated H decreases as Beta parameters go up given an Alpha value. In contrast, the estimated H increases as Alpha parameters go up given a Beta value. For the real-world data, the 2011 daily Taiwan stock index was used and the estimated Hurst index was 0.21.

Many complex systems generate multifractal time series which are long-range cross-correlated. This paper introduces three multifractal cross-correlation analysis methods, such as multifractal cross-correlation analysis based on the partition function approach (MFXPF), multifractal detrended cross-correlation analysis (MFDCCA) methods based on detrended fluctuation analysis (MFXDFA) and detrended moving average analysis (MFXDMA), which only consider one moment order. We do comparative analysis of the artificial time series (binomial multiplicative cascades and Cantor sets with different probabilities) by these methods. Then we do a feasibility test of the fixed threshold target detection within sea clutter by applying the multifractal cross-correlation analysis methods to the IPIX radar sea clutter data. The results show that it is feasible to use the method of the fixed threshold based on the multifractal feature parameter Δ f ( α ) by the MFXPF and MFXDFA-1 methods. At last, we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms, the detection parameters and the target detection methods within sea clutter in practice.

Fractal investigation of a signal often involves estimating its fractal dimension or Hurst exponent H when considered as a sample of a fractional process. Fractional Gaussian noise (fGn) belongs to the family of self-similar fractional processes and it is dependent on parameter H. There are variety of traditional methods for Hurst exponent estimation. Our novel approach is based on zero-crossing principle and signal segmentation. Thanks to the Bayesian analysis, we present a new axiomatically based procedure of determining the expected value of Hurst exponent together with its standard deviation and credible intervals. The statistical characteristics are calculated at the interval level at first and then they are used for the deduction of the aggregate estimate. The methodology is subsequently used for the EEG signal analysis of patients suffering from Alzheimer disease.

Detrended fluctuation analysis (DFA) is appropriate for the analysis of long-range correlation in nonstationary time series. In this study, DFA was used to study electroencephalography (EEG) fluctuations in order to assess the depth of anesthesia (DOA) and measure the level of consciousness. The fluctuation function F(s) was calculated. The distribution of F(s) in segments was used to classify anesthesia state levels into awake, light, moderate, and deep states. A linear fit of F(s) versus s in each segment was performed. Finally, the point at which the fitted line crossed the defined line divided the four zones corresponding to the four states of DOA from 100 to 0 in the coordinate system. Experimental results demonstrate that the proposed method can accurately identify the states of DOA based on EEG signals. The ranges of DOA values can be extended through adjustable parameters, improving the adaptability of the algorithm. The results are close to the bispectral index values, which can be used to identify anesthesia states. The proposed DFA method is effective for monitoring DOA.

Interaction patterns among different warehouses could make the warehouse-out behavioral sequences less predictable. We firstly take a coupling detrended fluctuation analysis on the warehouse-out quantity, and find that the multivariate sequences exhibit significant coupling multifractal characteristics regardless of the types of steel products. Secondly, we track the sources of multifractal warehouse-out sequences by shuffling and surrogating original ones, and we find that fat-tail distribution contributes more to multifractal features than the long-term memory, regardless of types of steel products. From perspective of warehouse contribution, some warehouses steadily contribute more to multifractal than other warehouses. Finally, based on multiscale multifractal analysis, we propose Hurst surface structure to investigate coupling multifractal, and show that multiple behavioral sequences exhibit significant coupling multifractal features that emerge and usually be restricted within relatively greater time scale interval.