Search

Mono- and multi-fractal geometry have been used to explore the surface characteristics of scanning electron microscopy (SEM) micrographs of the SnS films with thicknesses of 100 nm (SnS1) to 600 nm (SnS4), respectively. For this investigation, the SnS thin films have been grown on fluorine-doped tin oxide (FTO)-coated glass substrate through the thermal evaporation route, and surface morphologies are captured by SEM. Two-dimensional multi-fractal detrended fluctuation analysis (MFDFA) based on the partition function is used to examine whether the surfaces have a multi-fractal nature or not. The partition function is applied to extract the generalized Hurst exponent from the segment size. It has been found that surfaces with higher surface roughness induce substantial nonlinearity and a wider width of the multi-fractal spectrum. The multi-fractal spectrum acquired from the analysis of the geometry and shape of the singularity spectrum is used to quantify the irregularity and complexity of surfaces. Minkowski functionals (MFs) parameters such as volume, boundary, and connectivity were measured for each thin film. Moreover, we tried to correlate the electrical conductivity with the mono- and multi-fractal parameters such as fractal dimension (D f), singularity strength function (Δα), singularity spectrum Δf(α), and it is observed that the conductivity of a thin film decreases with decreasing fractal dimension. The minimum (maximum) resistivity (conductivity) was observed for the surface having a larger fractal dimension. The present investigation suggests that such SnS surfaces, having minimal resistivity and maximum conductivity on the roughest surface, indicate enhanced light trapping capacity and can be utilized as active layers for advanced optoelectronics devices. [ABSTRACT FROM AUTHOR]

Abstract Following the new advances in encryption and network computing, Bitcoin emerged as a private sector system facilitating peer-to-peer exchange via distributed ledgers based on blockchains, driving a transformational change towards a global economy outside the core financial system. The main purpose of this paper is to examine the multifractal properties of the Bitcoin price using high frequency data. The methods used are the wavelet transform modulus maxima and the multifractal detrended fluctuation analysis. The results indicate that Bitcoin exhibits a large degree of multifractality in all examined time intervals, and the main source of multifractality is attributed to the high kurtosis and the fat distributional tails of the series returns. Highlights • Encryption & network computing enabled a transformational change in markets via Bitcoin. • We explore the fractal dynamics of Bitcoin using high frequency data. • A novel hybrid of wavelet modulus maxima & detrended fluctuation analysis is used. • Fractality is observed in all time intervals. • The main drivers are high kurtosis & fat distributional tails. [ABSTRACT FROM AUTHOR]

Abstract Detrended Fluctuation Analysis has been used in several fields of science to study the statistical properties of trend stationary and nonstationary time-series. Its application to financial data has produced important results concerning long-range correlations and long-memory. However, these results may be contaminated if the researcher attributes to nonstationary trends the effect of stationary trends with endogenous structural breaks. Our paper proposes a modified DFA model where boxes to determine local trends are replaced by endogenous structural break windows. We also allow local trends fitted by quadratic functions and use squared residuals in place of patchy standard deviations to study the magnitude of the power-law exponent. The results show that our modified DFA model performs better than the fixed length alternatives originally proposed, and is, therefore, a suitable model to fit with financial data. Consistently with previous findings, our results show positive long-range correlation in all indices with the higher value for emerging markets. Highlights • Quadratic functions with negative concavity track integrated price returns. • Squared residuals yield better fits than average variances about the detrended walk. • Endogenous structural breaks yield better forecasts than equal length alternatives. • Data fitted by power-law distributions after the first few observations. • Crossover value of 0.5 reached for samples of at least four years of daily data. [ABSTRACT FROM AUTHOR]

Abstract By employing Detrended Fluctuation Analysis (DFA), which has been established as a standard method to investigate long range correlations in nonstationary time series, we study the temporal correlations between the magnitudes of the earthquakes that occurred before the recent deadly Mexico M8.2 earthquake on 7 September 2017 in Chiapas region. Our aim here is to shed light on the origin of the following precursory phenomenon found in our previous publication (Sarlis et al., 2018): Upon considering the analysis of seismicity in the new time domain termed natural time, it was shown that the entropy change of seismicity under time reversal exhibited an important minimum almost 3 months before this major earthquake. Here the application of DFA to earthquake magnitude time series reveals that this minimum of the entropy change of seismicity is preceded as well as followed by characteristic changes of temporal correlations between earthquake magnitudes, which are quantified by the DFA exponent α. In particular, before this minimum the long range correlations breakdown to an almost random behavior possibly turning to anticorrelation (α ≤ 0. 5) while after the minimum (and before the major M8.2 earthquake) long range correlations develop with an exponent α between 0.6 and 0.7. Highlights • DFA reveals precursory changes in the correlations between earthquake magnitudes. • The origin of the entropy change before the M8.2 earthquake is investigated. • DFA exponent minimizes just before the minimum of the M8.2 precursory entropy change. [ABSTRACT FROM AUTHOR]

Abstract We present a novel approach in the research field of price–trading in stock markets. We consider the effect of trading volume (related with liquidity) on the dynamic dependence of time series, using data from the Portuguese stock market, with both listed and non-listed firms in the main index. We use detrended fluctuation analysis, with a sliding windows approach, to estimate the dynamic dependence of shares. We found two interesting and related features: firms listed in the main index have results more centred at the 0.5 level; exponents' volatility is less in the second half of the sample, after the most severe period of the Eurodebt crisis. Then, we relate this dependence with trading volume, with detrended cross-correlation analysis and the respective correlation coefficient. We found that for firms listed in the main index, some show evidence of negative correlations while for non-listed firms, most of the shares have the same results. We conclude that the lack of liquidity could be related to increased dependence. An interesting feature found is that some firms have a positive correlationship between the variables, but all those firms work with natural resources in their activities, which could mean that other factors influence their dependence patterns. Highlights • A novel approach is presented to analyse the relationship between price and trading. • We used a sliding windows approach, to evaluate dependence evolution. • We make the correlation between (dynamical) dependence and trading volume. • Results show the importance of lack of liquidity in stock market dependence. [ABSTRACT FROM AUTHOR]

Abstract An experimental investigation on the self-excited spiky oscillations in a glow discharge plasma device is presented. The system showed a continuous transition from chaotic bursting to chaotic spiking states with the increase in the applied discharge voltage at a particular pressure. Below a threshold discharge voltage, the system exhibits a fixed point dynamical behaviour and with the increase in the discharge voltage bursting type oscillations appear which are identified as "fold/fold circle" type. The occurrence of the relaxation type spiky oscillations is attributed to the formation and disruption of anode double layer. The burst phases occurred intermittently and the frequency of their occurrence increased with increase in the discharge voltage and finally the oscillation turned into spiking behaviour. The intermittent oscillations manifested the scaling law of the average laminar phase with respect to the change in the discharge voltage. The scaling law of the intermittent oscillations was similar to type III intermittency. During the transition, the system changes its behaviour from long range correlation to long range anti correlation. Detrended fluctuation analysis technique has been used to identify the nature of long range correlations. We found that bursting oscillations show scale invariant, long-range correlation behaviour whereas spiking oscillations show scale invariant, long range anti correlation behaviour. Highlights • Transition from chaotic bursting to chaotic spiking behaviour is observed. • Floating potential fluctuations are intermittent in nature. • We found transition from long range correlation to long range anti correlation behaviour. • Long range correlation behaviour investigated using detrended fluctuation analysis. [ABSTRACT FROM AUTHOR]

Based on the detrended fluctuation analysis (DFA), we address the problem of recognizing the electrical activity of the brain associated with movements of the right arm and the imagination of this procedure. In experiments with untrained volunteers, we show the possibility to distinguish between the related EEG patterns. We also demonstrate significant distinctions in the scaling features between background records and EEG signals associated with mental intentions that can be transformed to control commands for brain–computer interfaces. This effect is observed in many EEG channels, although individual features of subjects provided various distributions of brain areas with the most prominent differences. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The analysis of stock markets’ behaviour remains a very interesting issue, because it can give investors information about where to apply their money. In this context, a dynamic analysis of 18 Eastern European stock markets is performed, using a sliding windows detrended fluctuation analysis, which will fill a gap in the literature with the inclusion in this study of a larger sample. The results show that most indices are distant from the absence of long-range dependencies, which could be seen as inefficiency. Nevertheless, some countries show a decrease in dependence levels over time, namely the Hungarian, Czech and Polish indices. When compared with other more developed markets, these and Latvia are the only ones to show similar behaviour, regarding the existence of long-range dependencies. This could be related to more developed economic structures as well as the financial system, probably associated with joining the European Union. However, other current European Union members, such as Bulgaria, Slovenia and Lithuania do not show this pattern. [ABSTRACT FROM AUTHOR]

The wind speed persistence is an important factor in the assessment of wind energy potential. In this paper, we explore the persistence of Mean Wind Speed (MWS) with many years of record using Detrended Fluctuation Analysis (DFA) over China. The results illustrate that there exist irregular high-frequency fluctuations for daily MWS anomaly records. Long-term persistence of MWS is found for all meteorological observed sites. We also make some numerical tests in order to verify the significance of long-term persistence by shuffling the data records many times. These facts prove that the MWS anomaly records have long-term persistence over all the stations in China. The mean value 0.64 in DFA-exponents for all stations over China is also obviously higher than the value 0.53 according to interval threshold of 95% confidence level after shuffling the MWS records many times. In addition, the values of scaling exponent vary from station to station over China. Long-term persistence of MWS in spatial distributions seems to be downward trends from east to west China. Many factors may affect long-term persistence of MWS such as southwest monsoon, Tibetan Plateau landform and atmosphere–ocean–land interaction and so on. Possible physical mechanism need further analysis in the future. [ABSTRACT FROM AUTHOR]

Autoregressive models are commonly used for modeling time-series from nature, economics and finance. This work explored simple autoregressive AR ( p ) models to remove long-term trends in detrended fluctuation analysis (DFA). Crude oil prices and bitcoin exchange rate were considered, with the former corresponding to a mature market and the latter to an emergent market. Results showed that AR ( p ) -based DFA performs similar to traditional DFA. However, the former DFA provides information on stability of long-term trends, which is valuable for understanding and quantifying the dynamics of complex time series from financial systems. [ABSTRACT FROM AUTHOR]

We study the temporal correlations in the evolution of the order parameter ϕ t for the Vicsek model with vectorial noise by estimating its Hurst exponent H with detrended fluctuation analysis (DFA). We present results on this parameter as a function of noise amplitude η introduced in simulations. We also compare with well known order–disorder phase transition for that same noise range. We find that – regardless of detrending degree – H spikes at the known coexistence noise for phase transition, and that this is due to nonstationarities introduced by the transit of the system between two well defined states with lower exponents. We statistically support this claim by successfully synthesizing equivalent cases derived from a transformed fractional Brownian motion (TfBm). [ABSTRACT FROM AUTHOR]

Basketball is one of the favourite sports in the United States and NBA the most popular basketball league in the world, followed not only by Americans but by fans everywhere. At present, people are increasingly interested in betting on sports in general and on basketball in particular. So analysis of trends in the results could be important for gamblers. In this paper, detrended fluctuation analysis is applied to 28 NBA teams, in order to understand if their results have (or not) any kind of memory. Our results show that all the teams are persistent in their results. Nevertheless, some teams have higher persistence than others, which could be important for gamblers in deciding how to bet. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Both sub-prime and Eurozone debt crisis problems caused severe financial crisis, which affected European markets in general, but particularly the banking sector. The continuous devaluation of bank shares in the financial sector caused a great decrease in market capitalization, and in citizen and investor confidence. Panic among investors led them to sell shares, while other agents took the opportunity to buy them. Therefore, the study of bank shares is important, particularly of their efficiency. In this paper, adopting a sliding windows detrended fluctuation approach, we analyse the efficiency concept dynamically with 63 European banks (both in and outside the Eurozone). The main results show that the crisis had an effect on changing the efficiency pattern. [ABSTRACT FROM AUTHOR]

We have carried out a detailed study of scaling region using detrended fractal analysis test by applying different forcing likewise noise, sinusoidal, square on the floating potential fluctuations acquired under different pressures in a DC glow discharge plasma. The transition in the dynamics is observed through recurrence plot techniques which is an efficient method to observe the critical regime transitions in dynamics. The complexity of the nonlinear fluctuation has been revealed with the help of recurrence quantification analysis which is a suitable tool for investigating recurrence, an ubiquitous feature providing a deep insight into the dynamics of real dynamical system. An informal test for stationarity which checks for the compatibility of nonlinear approximations to the dynamics made in different segments in a time series has been proposed. In case of sinusoidal, noise, square forcing applied on fluctuation acquired at P = 0.12 mbar only one dominant scaling region is observed whereas the forcing applied on fluctuation (P = 0.04 mbar) two prominent scaling regions have been explored reliably using different forcing amplitudes indicating the signature of crossover phenomena. Furthermore a persistence long range behavior has been observed in one of these scaling regions. A comprehensive study of the quantification of scaling exponents has been carried out with the increase in amplitude and frequency of sinusoidal, square type of forcings. The scalings exponent is envisaged to be the roughness of the time series. The method provides a single quantitative idea of the scaling exponent to quantify the correlation properties of a signal. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The outbreak of the Greek debt crisis caused turmoil in European markets and drew attention to the problem of public debt and its consequences. The increase in the return rates of sovereign debts was one of these consequences. However, like any other asset, sovereign debt returns are expected to have a memoryless behaviour. Analysing a total of 15 European countries (Eurozone and non-Eurozone), and applying a time-varying analysis of the Hurst exponent, we found evidence of long-range memory in sovereign bonds. When analysing the spreads between each bond and the German one, it is possible to conclude that Eurozone countries’ spreads show more evidence of long-range dependence. Considering the Eurozone countries most affected by the Eurozone crisis, that long-range dependence is more evident, but started before the crisis, which could be interpreted as possible speculation by investors. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the scaling exponent properties of mountainous river flow fluctuations by detrended fluctuation analysis (DFA). Streamflow data were collected continuously using Fluvial Acoustic Tomography System (FATS), which is a novel system for measuring continuous streamflow at high-frequency scales. The results revealed that river discharge fluctuations have two scaling regimes and scaling break. In contrast to the Ranting Curve method (RC), the small-scale exponent detected by the FATS is estimated to be 1.02 ± 0.42% less than that estimated by RC. More importantly, the crossover times evaluated from the FATS delayed approximately by 42 ± 21 hr ≈ 2–3 days than their counterparts estimated by RC. The power spectral density analysis assists our findings. We found that scaling characteristics information evaluated for a river using flux data obtained by RC approach might not be accurately detected, because this classical method assumes that flow in river is steady and depends on constructing a relationship between discharge and water level, while the discharge obtained by the FATS decomposes velocity and depth into two ratings according to the continuity equation. Generally, this work highlights the performance of FATS as a powerful and effective approach for continuous streamflow measurements at high-frequency levels. [ABSTRACT FROM AUTHOR]

We investigate the self-affinity of a fluid velocity time series in turbulent regime. We use the CFD OpenFoam library to simulate the flow of fluid in a duct with two obstacles injecting vorticity downstream. We calculated the fluid velocity in three sections in of the structure. The simulation presented more turbulences in sections further away from obstacles. We assess the self-affinity of properties of those sections by using the Detrended Fluctuation Analysis method. This scaling method presented two behaviors. First, a persistent behavior after passing through obstacles. Second, a sub-diffusive behavior in turbulent sections, presenting a long-range correlation α exponent ranging between 1.0 and 1.5. The findings suggest that chaotic states tend to follow a sub-diffusive process. [ABSTRACT FROM AUTHOR]

Football is a sport that moves thousands of people and millions of euros. Since 1983, several clubs entered the stock markets with shares, and now twenty two clubs are listed in the Stoxx Football Index. In this study, we analyse the behaviour of the return rates of such shares, with Detrended Fluctuation Analysis and Detrended Cross-Correlation Analysis (and its correlation coefficient). With Detrended Fluctuation Analysis, we are able to observe that the shares of several clubs are far from the behaviour of a random walk, which is expected by the theory. Using Detrended Cross-Correlation Analysis, we calculate the cross correlations of clubs’ returns with national indexes and then with the Stoxx Football Index. Although almost all of them are positive, they do not seem to be strong. [ABSTRACT FROM AUTHOR]

This paper explores a large collection of about 377,000 observations, spanning more than 20 years with a frequency of 30 min, of the streamflow of the Paglia river, in central Italy. We analyze the long-term persistence properties of the series by computing the Hurst exponent, not only in its original form but also under an evolutionary point of view by analyzing the Hurst exponents over a rolling windows basis. The methodological tool adopted for the persistence is the detrended fluctuation analysis (DFA), which is classically known as suitable for our purpose. As an ancillary exploration, we implement a control on the data validity by assessing if the data exhibit the regularity stated by Benford’s law. Results are interesting under different viewpoints. First, we show that the Paglia river streamflow exhibits periodicities which broadly suggest the existence of some common behavior with El Niño and the North Atlantic Oscillations: this specifically points to a (not necessarily direct) effect of these oceanic phenomena on the hydrogeological equilibria of very far geographical zones: however, such an hypothesis needs further analyses to be validated. Second, the series of streamflows shows an antipersistent behavior. Third, data are not consistent with Benford’s law: this suggests that the measurement criteria should be opportunely revised. Fourth, the streamflow distribution is well approximated by a discrete generalized Beta distribution: this is well in accordance with the measured streamflows being the outcome of a complex system. [ABSTRACT FROM AUTHOR]

Pedestrian stampede happened more and more often during these years, such as Love Parade disaster in Germany 2010, trampling in Shanghai bund 2014 and crowd stampede in pilgrimages. Love Parade disaster 2010 stands out for well recorded videos, which are HD quality and available for researchers. There were totally seven surveillance cameras capturing the whole festival progress and the video we study is just before the disaster happened. Pedestrian motion was special and a small disturbance would lead the group to an avalanche in this kind of critical situation. Here we focus on the individual movement pattern. The trajectories of each pedestrian involved were extracted by a mean-shift algorithm. We analyzed the space–time patterns of the pedestrians involved in the Love Parade stampede by using the detrended fluctuation analysis and the coefficient of variation. Our results reveal that the pedestrians’ movement in crowd-quakes is persistent in space, globally time-clusterized but locally regular or quasi-periodic behavior. Pedestrian movement was treated as stop and go state by point process-based representation. When the threshold increases, this means that the “go” state is longer and pedestrians keep on walking in several consecutive time frames; this is difficult in crowded situations and lead to special time-clustering behavior of the sequence of “go” events. The study reveals pedestrian motion characteristics in critical situations, which will enhance the understanding of pedestrian behaviors and supply early warning features for not only Love Parade Disaster, but also other similar large events. [ABSTRACT FROM AUTHOR]

Financial time series are usually analyzed by looking at the log-returns. This phenomenological approach is justified by the apparent multiplicativity of stochastic noise in the process. In fact, it hides the non-stationarity of the data. Here we shift the focus to the interplay of return and volume instead of log returns. We analyze statistics and causal relationships between the squared price and the volume increments of S&P 500 data. A new quantity, namely the ratio of price increments and the square root of the traded volume shows particular non-stationarity giving rise to a Hurst exponent of 0.65 by the so-called Moses effect. [ABSTRACT FROM AUTHOR]

The objective of this paper is to analyze if the Euro crisis, which started in 2009, changes the cross-correlation pattern of bank shares with the national stock indexes in both in Eurozone and non-Eurozone countries. We study all banks listed in the main stock indexes of European Union countries, applying the detrended cross-correlation coefficient. An increase in the correlation indicates that the banking sector now has a greater influence in the national index, while a decrease in the correlation means the opposite. Our results show that 19 of the 39 banks analyzed in the Eurozone increased their correlation with national indexes, whilst in the non-Eurozone countries this happened with 14 of the 24 studied banks. While some authors argue that the crisis may have been aggravated by the weight of banks in the economy, Eurozone policy makers should pay attention to this feature. [ABSTRACT FROM AUTHOR]

In many instances, the fluctuation function obtained from detrended fluctuation analysis (DFA) cannot be described by a uniform power-law function along scales. In fact, the manifestation of crossover scales may reflect the simultaneous action of different stochastic mechanisms displayed predominantly within certain scale ranges. This note proposes the use of a linear combination of power-law functions for adjusting DFA data. The idea is that each power-law function recast the dominance of certain stochastic mechanisms (e.g., the mean-reversion and long-term trends) at specific scale domains. Different values of the scaling exponents are numerically estimated by means of a nonlinear least-squares fitting of power-law functions. Examples of crude oil market and heart rate variability are discussed with some detail for illustrating the advantages of taking a linear combination of power-law functions for describing scaling behavior from DFA. [ABSTRACT FROM AUTHOR]

The scaling behavior of the pixel fluctuations of encrypted images is evaluated by using the detrended fluctuation analysis based on wavelets, a modern technique that has been successfully used recently for a wide range of natural phenomena and technological processes. As encryption algorithms, we use the Advanced Encryption System (AES) in RBT mode and two versions of a cryptosystem based on cellular automata, with the encryption process applied both fully and partially by selecting different bitplanes. In all cases, the results show that the encrypted images in which no understandable information can be visually appreciated and whose pixels look totally random present a persistent scaling behavior with the scaling exponent α close to 0.5, implying no correlation between pixels when the DFA with wavelets is applied. This suggests that the scaling exponents of the encrypted images can be used as a perceptual security criterion in the sense that when their values are close to 0.5 (the white noise value) the encrypted images are more secure also from the perceptual point of view. [ABSTRACT FROM AUTHOR]

In this study, we analyzed the autocorrelation among four ultraviolet (UV) radiation data sets obtained at 305 nm, 320 nm, 340 nm, and 380 nm. The data were recorded at ground level at the INPE climate station in Natal, RN, Brazil, which is a site close to the equator. The autocorrelations were computed by detrended fluctuation analysis ( DFA ) to estimate the index α . We found that the ​fluctuations in the UV radiation data were fractal, with scale-free behavior at a DFA index α ≃ 0.7 . In addition, we performed a power law spectral analysis, which showed that the power spectrum exhibited a power law behavior with an exponent of β ≃ 0.45 . Given that the theoretical result is β = 2 α − 1 , these two results are in good agreement. Moreover, the application of the DFA ​method to the UV radiation data required detrending using a polynomial with an order of at least eight, which was related to the complex daily solar radiation curve obtained at ground level in a tropical region. The results indicated that the α exponent of UV radiation is similar to other climatic records such as air temperature, wind, or rain, but not solar activity. [ABSTRACT FROM AUTHOR]

Detrended Fluctuation Analysis is a widely used method, which aims at assessing the level of self-similarity in time series. This method analyzes the diffusion properties of the signal, by computing the linear regression slope in the diffusion plot, representing in log–log coordinates the relationship between the variability of the signal and the length of the intervals over which this variability is computed. We compare in this paper the results obtained with logarithmically spaced and evenly spaced diffusion plots. The study shows the substantial benefits of evenly spacing, especially in the reduction of the variability of estimation. [ABSTRACT FROM AUTHOR]

We investigate here the effect of urbanization on the temporal behavior of streamflow records. To this end, we analyzed daily streamflow records from 22 urban basins using the scaling exponents for long-term correlated records and the multifractality strength. Additionally, we separated the streamflow into fast and slow components and performed the analysis separately on each of these time series. Overall, results indicate that in the most urbanized basins, with percent impervious cover greater than 25, the long-term correlation exponents for streamflow are generally lower than in the least urbanized basins (percent impervious cover less than 10), while the multifractality strength does not seem to be appreciably affected by the urbanization process. Based on the correlation exponents, we also found that in the most urbanized basins streamflow records tend to be more similar to quickflow and precipitation than in the least urbanized basins. Thus, the loss of long-term persistence in the most urbanized basins may be explained by their lesser ability, due to the combined presence of impervious surfaces and conventional stormwater infrastructure, to filter the precipitation forcing. We conclude that the correlation exponents can be useful for assessing the temporal alteration of streamflow in urban basins. [ABSTRACT FROM AUTHOR]

In this work we study the long-term correlations in the satellite daily number of hot pixels recorded in the Brazilian Amazon during the period 1999–2012. While the highest peak in daily hot pixel frequencies occurred in 2007, coincident with a severe drought, for other intense droughts such as that occurred in 2005 (one-in-a-hundred year event for its high severity) and 2010, the corresponding number of hot pixels recorded was compatible or lower than that reached during e.g. 2004, with no reported severe drought. On the other hand, we find that the most severe droughts coincide with the peaks of the Detrended Fluctuation Analysis (DFA) scaling exponent of the time series of the daily anomalies in hot pixels. This finding is striking because it highlights the effectiveness of the DFA in disclosing that long-term hot pixel anomaly correlations are clearly associated with the drought events, that were not identifiable by examining hot pixel frequencies of the original time series. The dynamics of the time series of daily anomalies in hot pixels is, therefore, influenced by drought events. The coincidence of the peaks of the scaling exponent with drought events suggests the increase of the persistence of the hot pixel time series during the driest periods. [ABSTRACT FROM AUTHOR]

The goal of the paper is to examine the auto-correlation properties for time series of the news flow intensity using different methods, such as the fluctuation analysis, the detrended fluctuation analysis and the detrending moving average analysis. Empirical findings for news analytics data show the presence of long-range correlations for the time series of news intensity data. [ABSTRACT FROM AUTHOR]

Fractal scaling patterns, which entail a power-law relationship between magnitude of fluctuations in a variable and the scale at which the variable is measured, have been found in many aspects of human behavior. These findings have led to advances in behavioral models (e.g. providing empirical support for cascade-driven theories of cognition) and have had practical medical applications (e.g. providing new methods for early diagnosis of medical conditions). In the present paper, fractal analysis is used to investigate whether similar fractal scaling patterns exist in inter-click interval and peak–peak amplitude measurements of bottlenose dolphin click trains. Several echolocation recordings taken from two male bottlenose dolphins were analyzed using Detrended Fluctuation Analysis and Higuchi’s (1988) method for determination of fractal dimension. Both animals were found to exhibit fractal scaling patterns near what is consistent with persistent long range correlations. These findings suggest that recent advances in human cognition and medicine may have important parallel applications to echolocation as well. [ABSTRACT FROM AUTHOR]

Many processes in nature are governed by nonlinear mechanisms that are frequently superposed by pronounced linear components. To characterize such complex dynamics it is desirable to disentangle linear and nonlinear features in empirical data. Quantitative nonlinear measures are also influenced by linear properties of the signals and, for the univariate case, Fourier transform surrogates do not represent properly the null hypothesis of zero nonlinear features. Here we elaborate on the application of a recently published method in Fourier space that does not suffer from comparison with inappropriate surrogate data and that reveals with high sensitivity correlations between Fourier phases and amplitudes. In addition, we propose a simple pre-processing procedure that avoids the mixing of linear and nonlinear features when applying conventional nonlinear measures, which can drastically increase the sensitivity of the statistical evaluation and avoids numerical problems associated with surrogate data. We test our proposal on data derived from numerical models and we analyze electroencephalographic recordings from epilepsy patients as well as heart rate signals from healthy subjects before and during meditation. [ABSTRACT FROM AUTHOR]

The time-singularity multifractal spectrum distribution (TS-MFSD) generalizes the singularity spectrum in a time-varying framework. In this paper, a new method to compute MFSD based on detrended fluctuation analysis (DFA-MFSD) is introduced. We relate DFA-MFSD method to the standard partition function based multifractal spectrum distribution formalism, and prove that both approaches are equivalent for fractal time series with compact support. Furthermore, we find that DFA-MFSD has equivalent results, better mathematic foundation, less computational cost and is more adapted for fractal time series with arbitrary length, compared with MFSD based on wavelet transform modulus maxima (WTMM-MFSD). By analyzing several examples, this paper shows that DFAm-MFSD with different polynomial fitting orders can reliably determine the time-varying multifractal scaling behavior of time series, including processes embodying chirp-type or oscillating singularities. To illustrate these results, simulations are executed using binomial multiplicative cascades, wavelet series and real sea clutter, and simulations indicate that DFA m -MFSD benefits from excellent theoretical and practical performances. [ABSTRACT FROM AUTHOR]

In this study, we investigate the self-affinity of time series of thermal radiation from two fuels, natural gas (NG) and acetylene (AC), enriched with oxygen at 21%, 23% and 25% concentrations during the combustion process. We used the detrended fluctuation analysis method to evaluate the burning process of these fuels. We found a well-defined self-affine aspect for these gases in this dynamic process. Using the proposed method, we were able to characterize the time series of NG as a sub-diffusive process and the time series of AC as a process with persistent self-affinity. [ABSTRACT FROM AUTHOR]

As an emerging financial market, the trading value of carbon emission trading market has definitely increased. In recent years, the carbon emission allowances have already become a way of investment. They are bought and sold not only by carbon emitters but also by investors. In this paper, we analyzed the price fluctuations of the European Union allowances (EUA) futures in European Climate Exchange (ECX) market from 2007 to 2011. The symmetric and power-law probability density function of return time series was displayed. We found that there are only short-range correlations in price changes (return), while long-range correlations in the absolute of price changes (volatility). Further, detrended fluctuation analysis (DFA) approach was applied with focus on long-range autocorrelations and Hurst exponent. We observed long-range power-law autocorrelations in the volatility that quantify risk, and found that they decay much more slowly than the autocorrelation of return time series. Our analysis also showed that the significant cross correlations exist between return time series of EUA and many other returns. These cross correlations exist in a wide range of fields, including stock markets, energy concerned commodities futures, and financial futures. The significant cross-correlations between energy concerned futures and EUA indicate the physical relationship between carbon emission and energy production process. Additionally, the cross-correlations between financial futures and EUA indicate that the speculation behavior may become an important factor that can affect the price of EUA. Finally we modeled the long-range volatility time series of EUA with a particular version of the GARCH process, and the result also suggests long-range volatility autocorrelations. [ABSTRACT FROM AUTHOR]

The detrended fluctuation analysis (DFA) and the multifractal DFA (MF-DFA) techniques are employed to characterize the pseudorapidity ( η ) distribution of charged mesons produced in 28 Si+Ag/Br interaction at 14.5 GeV/nucleon and 32 S+Ag/Br interaction at 200 GeV/nucleon. Various multifractal parameters are calculated and compared with a Monte-Carlo simulation based on the ultra-relativistic quantum molecular dynamics (UrQMD) model. The results of this analysis show that the single particle distributions in both experiments and in their respective UrQMD simulations are multifractal in nature. The differences between the experiment and corresponding simulation however, are not always very significant. But the present results are significantly different from those obtained by using other conventional methods of multifractal analysis. The observations also indicate that the detrended multifractal analysis might be an efficient tool for characterizing the multiparticle emission data, but the method requires some improvement so that it can differentiate between the non-statistical signal and the statistical noise. [ABSTRACT FROM AUTHOR]

In this paper the two dimensional model of the investment in shares is presented. The shares prices from five different world stock exchanges (New York, London, Frankfurt, Honk Kong, and Sydney) are examined. The copula functions are used to model the risk of investment. The Hurst threshold exponent derived from the local Detrended Fluctuation Analysis is used to determine the safe investment portfolios with no extreme drops in shares prices. The most important result states that the threshold value is not universal for different markets, however, it is influenced by the subsequent level of market freedom. It was shown, that the level, relatively larger in US, UK, and Australia than in Germany and China, affects the Hurst exponent threshold value. [ABSTRACT FROM AUTHOR]

Despite its solid foundations, multifractal analysis is still a challenging task. The ‘inversed’ singularity spectrum is a major pitfall in standard multifractal analyses especially for empirical signals. To resolve this issue, we identified the fan-like convergent geometry of scaling functions yielding a limit value (termed focus ) for all moments at the largest scale. Building on this behavior of scaling, we introduce the novel concept of focus-based multifractal formalism. It relies on enforcing this universal behavior when the moment-wise scaling exponents are assessed for the scaling functions. Besides developing focus-based variants of the established multifractal detrended fluctuation analysis and the wavelet leader method, we present a novel analytical tool of multifractal signal summation conversion. All methods are extensively tested on exact multifractal signals synthesized by the generalized binomial multifractal model in terms of precision and incidence of ‘inversed’ singularity spectra. Our focus-based variants never yielded ‘inversed’ spectra and their precision was found similar to that of standard methods. Our approach allowed computing a moment-wise and a global error parameter describing the impact of finite size effect and degree of multifractality as compared to that of the fitted exact multifractal model. We demonstrate that the standard approach to multifractal analyses contains a central element that is essentially monofractal due to its regression scheme assessing the scaling exponents for each and every moment, separately. Hence these methods can yield reliable estimates only for ideally behaving multifractal signals. In contrast, our focus-based variants due to their genuine multifractal model fitting always yield reliable estimates accompanied by goodness-of-fit statistics. The presented novel multifractal tools offer means of dealing with the consequences of endogenous impurities of potentially multifractal empirical signals. [ABSTRACT FROM AUTHOR]

In financial markets, the weak form of the efficient market hypothesis implies that price returns are serially uncorrelated sequences. In other words, prices should follow a random walk behavior. Recent developments in evolutionary economic theory (Lo, 2004) have tailored the concept of adaptive market hypothesis (AMH) by proposing that market efficiency is not an all-or-none concept, but rather market efficiency is a characteristic that varies continuously over time and across markets. Within the AMH framework, this work considers the Dow Jones Index Average (DJIA) for studying the deviations from the random walk behavior over time. It is found that the market efficiency also varies over different time scales, from weeks to years. The well-known detrended fluctuation analysis was used for the characterization of the serial correlations of the return sequences. The results from the empirical showed that interday and intraday returns are more serially correlated than overnight returns. Also, some insights in the presence of business cycles (e.g., Juglar and Kuznets) are provided in terms of time variations of the scaling exponent. [ABSTRACT FROM AUTHOR]

In our work copula functions and the Hurst exponent calculated using the local Detrended Fluctuation Analysis (DFA) were used to investigate the risk of investment made in shares traded on the Warsaw Stock Exchange. The combination of copula functions and the Hurst exponent calculated using local DFA is a new approach. For copula function analysis bivariate variables composed of shares prices of the PEKAO bank (a big bank with high capitalization) and other banks (PKOBP, BZ WBK, MBANK and HANDLOWY in decreasing capitalization order) and companies from other branches (KGHM—mining industry, PKNORLEN—petrol industry as well as ASSECO—software industry) were used. Hurst exponents were calculated for daily shares prices and used to predict high drops of those prices. It appeared to be a valuable indicator in the copula selection procedure, since Hurst exponent’s low values were pointing on heavily tailed copulas e.g. the Clayton one. [ABSTRACT FROM AUTHOR]

The multifractal detrended fluctuation analysis technique is employed to analyze the time series of gold consumer price index (CPI) and the market trend of three world’s highest gold consuming countries, namely China, India and Turkey for the period: 1993–July 2013. Various multifractal variables, such as the generalized Hurst exponent, the multifractal exponent and the singularity spectrum, are calculated and the results are fitted to the generalized binomial multifractal (GBM) series that consists of only two parameters. Special emphasis is given to identify the possible source(s) of multifractality in these series. Our analysis shows that the CPI series and all three market series are of multifractal nature. The origin of multifractality for the CPI time series and Indian market series is found due to a long-range time correlation, whereas it is mostly due to the fat-tailed probability distributions of the values for the Chinese and Turkey markets. The GBM model series more or less describes all the time series analyzed here. [ABSTRACT FROM AUTHOR]

Abstract: We develop a criterion based on a brute-force algorithm to systematically determine optimal fitting regions for fluctuation functions in Detrended Fluctuation Analysis (DFA) and Multifractal Detrended Fluctuation Analysis (MF-DFA). We analyze and compare results with several artificially generated time series with known parameters as illustrative examples of this technique. We show that crossover time scales can also be objectively and efficiently estimated using the introduced algorithm. Finally, we employ the proposed methodology to study the scaling behavior of a natural time series: monthly sunspot data previously filtered with empirical mode decomposition (EMD); in this case we find results comparable with those found in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze empirical data, accounting for coordination processes between complex systems (bimanual coordination, interpersonal coordination, and synchronization with a fractal metronome), by using a recently proposed method: detrended cross-correlation analysis (DCCA). This work is motivated by the strong anticipation hypothesis, which supposes that coordination between complex systems is not achieved on the basis of local adaptations (i.e., correction, predictions), but results from a more global matching of complexity properties. Indeed, recent experiments have evidenced a very close correlation between the scaling properties of the series produced by two coordinated systems, despite a quite weak local synchronization. We hypothesized that strong anticipation should result in the presence of long-range cross-correlations between the series produced by the two systems. Results allow a detailed analysis of the effects of coordination on the fluctuations of the series produced by the two systems. In the long term, series tend to present similar scaling properties, with clear evidence of long-range cross-correlation. Short-term results strongly depend on the nature of the task. Simulation studies allow disentangling the respective effects of noise and short-term coupling processes on DCCA results, and suggest that the matching of long-term fluctuations could be the result of short-term coupling processes. [Copyright &y& Elsevier]

Abstract: In this paper we focus on the statistical distribution of time intervals between geomagnetic reversals. Recently the Tsallis distribution was pointed out as a possible alternative to previous proposals. We have performed statistical tests to further prove this and find the parameters of the Tsallis distribution that better fit the data. Additionally we have analyzed the correlation of time intervals between consecutive reversals to show the presence of memory effects on the mechanism that generates them, as could be expected for some Tsallis systems. [Copyright &y& Elsevier]

Abstract: Detrended Fluctuation Analysis (DFA) is a method that has been frequently used to determine the presence of long-range correlations in human and animal behaviors. However, according to previous authors using statistical model systems, in order to correctly use DFA different aspects should be taken into account such as: (1) the establishment by hypothesis testing of the absence of short term correlation, (2) an accurate estimation of a straight line in the log–log plot of the fluctuation function, (3) the elimination of artificial crossovers in the fluctuation function, and (4) the length of the time series. Taking into consideration these factors, herein we evaluated the presence of long-range correlation in the temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus). In our study, modeling the data with the general autoregressive integrated moving average (ARFIMA) model, we rejected the hypothesis of short-range correlations in all cases. We also observed that DFA was able to distinguish between the artificial crossover observed in the temporal pattern of locomotion of Japanese quail and the crossovers in the correlation behavior observed in mosquito larvae locomotion. Although the test duration can slightly influence the parameter estimation, no qualitative differences were observed between different test durations. [Copyright &y& Elsevier]

Abstract: While many microscopic models of traffic flow describe transitions between different traffic phases, such transitions are difficult to quantify in measured traffic data. Here we study long-term traffic recordings consisting of days of flow, density, and velocity time series with minute resolution from a Spanish motorway. We calculate fluctuations, cross-correlations, and long-term persistence properties of these quantities in the flow–density diagram. This leads to a data-driven definition of (local) traffic states based on the dynamical properties of the data, which differ from those given in standard guidelines. We find that detrending techniques must be used for persistence analysis because of non-stationary daily and weekly traffic flow patterns. We compare our results for the measured data with analysis results for a microscopic traffic model, finding good agreement in most quantities. However, the simulations cannot easily reproduce the congested traffic states observed in the data. We show how fluctuations and cross-correlations in traffic data may be used for prediction, i.e., as indications of increasing or decreasing velocities. [Copyright &y& Elsevier]

Abstract: We examine the scaling regime for the detrended fluctuation analysis (DFA)—the most popular method used to detect the presence of long-term memory in data and the fractal structure of time series. First, the scaling range for DFA is studied for uncorrelated data as a function of time series length and the correlation coefficient of the linear regression at various confidence levels. Next, a similar analysis for artificial short series of data with long-term memory is performed. In both cases the scaling range is found to change linearly—both with and . We show how this dependence can be generalized to a simple unified model describing the relation where ( ) stands for the Hurst exponent of the long range autocorrelated signal. Our findings should be useful in all applications of DFA technique, particularly for instantaneous (local) DFA where a huge number of short time series has to be analyzed at the same time, without possibility of checking the scaling range in each of them separately. [Copyright &y& Elsevier]