Application Of Detrended Fluctuation Analysis Research Articles

Self-potential time series reveal emergent behavior in soil organic matter dynamics

The active cycling of carbon between soil organic matter and the atmosphere is of critical importance to global climate change. An extensive body of research exists documenting the capricious nature of soil organic matter (SOM) dynamics, which is symptomatic of an intricate network of interactions between diverse groups of heterotrophic microorganisms, complex organic substrates, and highly variable local environmental conditions. These attributes are consistent with elements of complex system theory and the temporal evolution of otherwise unpredictable patterns of behavior that emerge from long range dependency on initial conditions. Here we show that vertical depth profile of self-potential (SP) time series measurements responds in a quantitative manner to variations in soil moisture, SOM concentrations, and relative rates of microbial activity. Application of detrended fluctuation analysis (DFA) of self potential time series data is shown additionally to reveal the presence of long-range dependence and emergence of anomalous electrochemical diffusion behavior, both of which diminish with depth as SOM specific energy densities decline.

Application of Detrended Fluctuation Analysis and Yield Stability Index to Evaluate Near Infrared Spectra of Green and Roasted Coffee Samples

Coffee quality, and therefore its price, is determined by coffee species and varieties, geographic location, the method used to process green coffee beans, and particularly the care taken during coffee production. Determination of coffee quality is often done by the nondestructive and fast near infrared spectroscopy (NIRS), which provides a huge amount of data about the samples. NIRS data require sophisticated, multivariate data analysis methods, such as principal component analysis, or linear discriminant analysis. Since the obtained data are a set of spectra, they can also be analyzed by signal processing methods. In the present study, the applications of two novel methods, detrended fluctuation analysis (DFA) and yield stability index (YSI), is introduced on NIR spectra of different roasting levels of coffee samples. Fourteen green coffee samples from all over the world have been roasted on three different levels and their NIR spectra were analyzed. DFA successfully differentiated the green samples from the roasted ones, however, the joint analysis of all samples was not able to differentiate the roasting levels. On the other hand, DFA successfully differentiated the roasting levels on samples level, which was strengthened by a 100% accurate agglomerative hierarchical clustering. YSI was first used in NIR signal processing and was able to detect that a light roast is the most stable among all roasting levels. Future research should focus on the application of DFA in terms of the analysis of the effects of other transformation methods of the spectra.

The application of detrended fluctuation analysis to assess physical characteristics of the human cell line ECV304 following toxic challenges

In this paper we present a non-contact, impedance-based sensor system capable of characterizing the toxic response of cells to three different types of toxin. ECV304 cells were treated with 1 mM Hydrogen peroxide, 5% Dimethyl Sulfoxide, and 10 μg/ml saponin. Impedance spectroscopy was performed over a 2 h period on the cells within a commercial cell growth chamber, positioned on a pair of measurement electrodes, at frequencies between 200 and 830 kHz at 10 kHz intervals. Analysis of the impedance data was undertaken using the feature-extraction technique, Detrended Fluctuation Analysis (DFA). DFA scales the autocorrelation of a non-stationary signal, such as those generated using impedance spectroscopy for cytotoxicity testing. The correlation between the average fluctuation of the signal, F(n) (and scaling exponent, α) and a measurement of the cell size from image analysis was evaluated. The results showed that F(n) and α were strongly related to the changes of the morphological size of the cells. The results demonstrated that non-contact impedance spectroscopy, coupled with DFA can be used to monitor cell size in real time.

Investigation of the temporal correlations between earthquake magnitudes before the Mexico M8.2 earthquake on 7 September 2017

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.

Power considerations for the application of detrended fluctuation analysis in gait variability studies.

The assessment of gait variability using stochastic signal processing techniques such as detrended fluctuation analysis (DFA) has been shown to be a sensitive tool for evaluation of gait alterations due to aging and neuromuscular disease. However, previous studies have suggested that the application of DFA requires relatively long recordings (600 strides), which is difficult when working with clinical populations or older adults. In this paper we propose a model for predicting DFA variance in experimental data and conduct a Monte Carlo simulation to estimate the sample size and number of trials required to detect a change in DFA scaling exponent. We illustrate the model in a simulation to detect a difference of 0.1 (medium effect) between two groups of subjects when using short gait time series (100 to 200 strides) in the context of between- and within-subject designs. We assumed that the variance of DFA scaling exponent arises due to individual differences, time series length, and experimental error. Results showed that sample sizes required to achieve acceptable power of 80% are practically feasible, especially when using within-subject designs. For example, to detect a group difference in the DFA scaling exponent of 0.1, it would require either 25 subjects and 2 trials per subject or 12 subjects and 4 trials per subject using a within-subject design. We then compared plausibility of such power predictions to the empirically observed power from a study that required subjects to synchronize with a persistent fractal metronome. The results showed that the model adequately predicted the empirical pattern of results. Our power simulations could be used in conjunction with previous design guidelines in the literature when planning new gait variability experiments.

Altered temporal correlations in resting-state connectivity fluctuations in children with reading difficulties detected via MEG

In this study we investigate systematic patterns of rapidly changing sensor-level interdependencies in resting MEG data obtained from 23 children experiencing reading difficulties (RD) and 27 non-impaired readers (NI). Three-minute MEG time series were band-passed and subjected to blind source separation (BSS) prior to estimating sensor interdependencies using the weighted phase synchronization measure (wPLI). Dynamic sensor-level network properties were then derived for two network metrics (global and local efficiency). The temporal decay of long-range temporal correlations in network metrics (LRTC) was quantified using the scaling exponent (SE) in detrended fluctuation analysis (DFA) plots. Having established the reliability of SE estimates as robust descriptors of network dynamics, we found that RD students displayed significantly reduced (a) overall sensor-level network organization across all frequency bands (global efficiency), and (b) temporal correlations between sensors covering the left temporoparietal region and the remaining sensors in the β3 band (local efficiency). Importantly, both groups displayed scale-free global network connectivity dynamics. The direct application of DFA to MEG signals failed to reveal significant group differences. Results are discussed in relation to prior evidence for disrupted temporoparietal functional circuits for reading in developmental reading disability.

Novel application of detrended fluctuation analysis for state estimation using synchrophasor measurements

The phasor measurement unit (PMU), with its ability to directly calculate synchronized positive sequence voltages and currents (magnitude and phase), offers a more current and accurate view of the power system compared to that provided by traditional measurements and state estimation (SE). However, the high-resolution data, provided at rates of 50 Hz and 60 Hz (dependant on nominal frequency), capture any transient or dynamic events occurring on the network, potentially distorting the intended steady-state view at various points of the power system. In this paper we propose the use of detrended fluctuation analysis (DFA) to detect and isolate such events for alternative investigation. Comparisons are made between the state estimator and installed PMUs on the high-voltage transmission system of Great Britain.

Detrended Fluctuation Analysis: A Scale-Free View on Neuronal Oscillations

Recent years of research have shown that the complex temporal structure of ongoing oscillations is scale-free and characterized by long-range temporal correlations. Detrended fluctuation analysis (DFA) has proven particularly useful, revealing that genetic variation, normal development, or disease can lead to differences in the scale-free amplitude modulation of oscillations. Furthermore, amplitude dynamics is remarkably independent of the time-averaged oscillation power, indicating that the DFA provides unique insights into the functional organization of neuronal systems. To facilitate understanding and encourage wider use of scaling analysis of neuronal oscillations, we provide a pedagogical explanation of the DFA algorithm and its underlying theory. Practical advice on applying DFA to oscillations is supported by MATLAB scripts from the Neurophysiological Biomarker Toolbox (NBT) and links to the NBT tutorial website http://www.nbtwiki.net/. Finally, we provide a brief overview of insights derived from the application of DFA to ongoing oscillations in health and disease, and discuss the putative relevance of criticality for understanding the mechanism underlying scale-free modulation of oscillations.

Characteristic time scales of electroencephalograms of narcoleptic patients and healthy controls

Sleep electroencephalograms (EEGs) typically showed correlated fluctuations that became random-like oscillations beyond a characteristic time scale. To investigate this behavior quantitatively, the detrended fluctuation analysis (DFA) was applied to EEGs of 10 narcoleptic patients ( 22.0 ± 4.0 yrs ; 6 males) and 8 healthy controls ( 24.0 ± 2.0 yrs ; 5 males). The characteristic time scales of the narcoleptics and controls were estimated as 1.8 ± 0.7 and 4.4 ± 1.2 s , respectively (significance level, p < 0.01 ). We further performed DFA of the EEGs segmented into 30 s epochs and found that the DFA scaling exponents increased in deep sleep stages. These results were verified with power spectrum and auto-correlation analysis, and reproduced by a mathematical model. We thus concluded that characteristics of EEGs of narcoleptic patients could be differentiated from those of healthy subjects, suggesting a potential application of DFA in diagnosing narcolepsy.

Response to Chastin et al.: ANALYSIS OF NONLINEAR PATTERNS OF ACTIVITY

Response to Chastin et al.: ANALYSIS OF NONLINEAR PATTERNS OF ACTIVITY

Stock Indices for Emerging Markets

In the last years a lot of attention was paid to the Hurst exponent and its application to predict prices in financial markets. In this study, we employ the Hurst exponent to quantify the long-term correlations. We use detrended fluctuation analysis (DFA) method to calculate the Hurst exponent, as it is known to be the most efficient [1]. The method itself is described in the next section. The application of DFA for studying the stock market behavior was initiated by Liu et al. [2]. They show that the S&P500 stock index exhibits weak long-range correlations. On the other hand, Grech and Pamula [3] and Grech and Mazur [4] employed the local Hurst exponent behavior in order to predict crashes on the financial market.

An empirical examination of detrended fluctuation analysis for gait data

Stride interval series exhibit statistical persistence, and detrended fluctuation analysis (DFA) is a routinely employed technique for describing this behavior. However, the implementation of DFA to gait data varies considerably between studies. We empirically examine two practical aspects of DFA which significantly affect the analysis outcome: the box size range and the stride interval series length. We conduct an analysis of their effect using stride intervals from 16 able-bodied adults, for overground walking, treadmill walking while holding a handrail, and treadmill walking without using a handrail. Our goal is to provide general guidelines for these two choices, with the aim of standardizing the application of DFA and facilitating inter-study comparisons. Based on the results of our analysis, we propose the use of box sizes from 16 to N / 9 , where N is the number of stride intervals. Moreover, for differentiating between normal and pathological walking with reasonable accuracy, we recommend a minimum of 600 stride intervals.

Fractional dynamic behavior in Forcados Oil Price Series: An application of detrended fluctuation analysis

Nigeria experienced a long history of macroeconomic instability since political independence. For many years, Nigerian policymakers had been unsuccessful in their attempts to manage the national economy to deal with macroeconomic instability. They have been accused of mismanagement and incompetence when it comes to preparation and execution of national budgets. In an effort to arrest this problem, the federal government recently introduced structure into public budgeting. A Fiscal Responsibility Act was passed to improve the budgetary process. Consistent with the law, policymakers are required to devise a process for forecasting revenue. Thus, with the help of experts from the International Monetary Fund, an ARMA(p,q) (autoregressive moving average) process was recommended. An ARMA model combines an autoregressive component which captures past values of a time series with a moving average component which captures past forecast errors associated with the time series. As a mono-cultural economy with crude oil as the main source of government revenue, an ARMA(p,q) process assumes that the oil price series is stationary with a short memory. In this paper, we set out to test for the presence of long memory or persistence in oil price series using weekly data from 1978 to 2007. The results of the detrended fluctuation analysis (DFA) suggest Nigeria's oil price series is anti-persistent. A Hurst exponent of 0.48 is indicative of a time series which is covariance stationary but mean-reverting. In other words, we can fit a stationary ARMA(p,q) model driven by fractional noise to the series. This implies that a low price level has a tendency to be followed by a high price level and vice versa. Thus, past price trends are more likely to change in the future. Moreover, the effect of shocks to the price system dies away in the long run. Therefore, the current revenue forecasting tool would need to be overhauled in the presence of price reversals. This is more critical in the face of constant disruptions to oil production in the Niger Delta where the Forcados variety is produced.

Detecting long-range correlation with detrended fluctuation analysis: Application to BWR stability

The aim of this paper is to explore the application of detrended fluctuation analysis (DFA) to study boiling water reactor stability. DFA is a scaling method commonly used for detecting long-range correlations in non-stationary time series. This method is based on the random walk theory and was applied to neutronic power signal of Forsmark stability benchmark. Our results shows that the scaling properties breakdown during unstable oscillations.

Detrended fluctuation analysis in x-ray photon correlation spectroscopy for determining coarsening dynamics in alloys

We study the dynamics of precipitate coarsening in phase-separating alloys at late stages of phase separation by x-ray photon correlation spectroscopy (XPCS). For analyzing time series of fluctuating speckle intensities from small-angle scattering of coherent x rays, the method of detrended fluctuation analysis (DFA), which is ideal for determining power-law correlations, is applied. We discuss the application of DFA with respect to XPCS data by means of simulated time series. In particular, the effects of different signal-to-noise ratios are examined. Results from measurements of the two model systems Al-6 at. % Ag at 140 degrees C and Al-9 at. % Zn at 0 degrees C are presented. Since the DFA effectively removes adulterating trends in the data, quantitative agreement with Monte Carlo simulations is obtained. It is verified that two different coarsening mechanisms are predominant in the two systems--coarsening either by diffusion of single atoms or by movement of whole precipitates.

Scaling properties of image textures: A detrending fluctuation analysis approach

The aim of this paper is to explore the application of detrended fluctuation analysis (DFA) to study roughness features of images. Unidimensional sequences at different image orientations are extracted and their average scaling exponent is estimated. In this form, the existence of anisotropies can be detected when considerable variations in the scaling exponent at different image orientation are observed. Different images from grass to solar granulation are analyzed and the underlying physics of such results is briefly commented.

Detrended fluctuation analysis of rainfall and streamflow time series

Several recent studies have shown that a remarkably wide variety of natural systems display fluctuations that may be characterized by long‐range power‐law correlations. Such correlations hint toward fractal geometry of the underlying dynamical system. Existence and determination of power‐law correlations would help to quantify the underlying process dynamics. Traditional time series analysis of rainfall, for example using spectral analysis, often produces spurious results due to the highly nonstationary nature of rainfall signals. Here we present some new results using detrended fluctuation analysis (DFA) to quantify the correlation properties of rainfall time series. The DFA allows the detection of long‐range correlations embedded in an apparently nonstationary time series and has been successfully applied to analyze highly nonstationary DNA sequences, heartbeat time series, and temperature fluctuations. Our analysis of rainfall data ranges from hourly to annual timescales for geographically and meteorologically distinct regions. Results show a common scaling behavior for all stations analyzed. Two distinct scaling regions are identified, one corresponding to short‐range and the other to long‐range correlations, on either side of a breakpoint. Additional synthetic experiments demonstrate that what controls the correlation structure is not the actual rainfall values but the pattern of alternating wet and dry spells. The application of DFA on streamflow reflects the fact that streamflow is characterized by smooth fluctuations compared to its driving process, rainfall. Our results highlight the dampening effect that the soil has on the rainfall correlations.