Detrended Fluctuation Analysis Method Research Articles

The Multifractal Phenomenon of Stock Price Caused by “Tesla Rights Defense Event”

In this paper, we explore the periodicity of the multifractal phenomenon of stock price caused by public relations events using the multifractal detrended fluctuation analysis (MF-DFA) method. The Tesla stock closing price in the context of the Tesla rights defense event is used to obtain the generalized Hurst exponent and multifractal spectrum. We find that the stock price exhibits multifractal characteristics. Afterwards, we conduct a multifractal time-varying analysis using high-frequency data for 12 time periods before and after the Tesla rights defense event, which happened on 19 April 2021. We calculate the [Formula: see text] and [Formula: see text] before and after the rights defense event to measure the degree of multifractal of Tesla stock price. In addition, we also compute the difference between the two [Formula: see text] and two [Formula: see text], which are regarded as [Formula: see text] and [Formula: see text]. The results show that the Tesla stock market efficiency degree raised as the period time increases until the eighth period. And after the eighth period, both [Formula: see text] and [Formula: see text] tend to be stable, and the degree of market efficiency caused by the Tesla rights defense event remains almost unchanged. In addition, we use three broad market indices in the context of the Russia–Ukraine conflict to test the universality. The three broad market indices are Dow Jones Industrial Average (DJIA), Shanghai Stock Exchange Composite Index (SSEC) and Nikkei 225 ETF (N225). The results demonstrate that with the extending of time period, [Formula: see text] and [Formula: see text] gradually stabilize, indicating that public memorability will diminish and the market efficiency almost remains unchanged.

Assessing cardiovascular stress based on heart rate variability in female shift workers: a multiscale-multifractal analysis approach.

Sleep-wake cycle disruption caused by shift work may lead to cardiovascular stress, which is observed as an alteration in the behavior of heart rate variability (HRV). In particular, HRV exhibits complex patterns over different time scales that help to understand the regulatory mechanisms of the autonomic nervous system, and changes in the fractality of HRV may be associated with pathological conditions, including cardiovascular disease, diabetes, or even psychological stress. The main purpose of this study is to evaluate the multifractal-multiscale structure of HRV during sleep in healthy shift and non-shift workers to identify conditions of cardiovascular stress that may be associated with shift work. The whole-sleep HRV signal was analyzed from female participants: eleven healthy shift workers and seven non-shift workers. The HRV signal was decomposed into intrinsic mode functions (IMFs) using the empirical mode decomposition method, and then the IMFs were analyzed using the multiscale-multifractal detrended fluctuation analysis (MMF-DFA) method. The MMF-DFA was applied to estimate the self-similarity coefficients, α(q, τ), considering moment orders (q) between -5 and +5 and scales (τ) between 8 and 2,048 s. Additionally, to describe the multifractality at each τ in a simple way, a multifractal index, MFI(τ), was computed. Compared to non-shift workers, shift workers presented an increase in the scaling exponent, α(q, τ), at short scales (τ < 64 s) with q < 0 in the high-frequency component (IMF1, 0.15-0.4 Hz) and low-frequency components (IMF2-IMF3, 0.04-0.15 Hz), and with q> 0 in the very low frequencies (IMF4, < 0.04 Hz). In addition, at large scales (τ> 1,024 s), a decrease in α(q, τ) was observed in IMF3, suggesting an alteration in the multifractal dynamic. MFI(τ) showed an increase at small scales and a decrease at large scales in IMFs of shift workers. This study helps to recognize the multifractality of HRV during sleep, beyond simply looking at indices based on means and variances. This analysis helps to identify that shift workers show alterations in fractal properties, mainly on short scales. These findings suggest a disturbance in the autonomic nervous system induced by the cardiovascular stress of shift work.

Multifractal analysis of maize and soybean DNA

This paper investigates the complexity of DNA sequences in maize and soybean using the multifractal detrended fluctuation analysis (MF-DFA) method, chaos game representation (CGR), and the complexity-entropy plane approach. The study aims to understand the patterns and structures of these DNA sequences, which can provide insights into their genetic makeup and improve crop yield and quality. The results show that maize and soybean DNA sequences exhibit fractal properties, indicating a complex and self-organizing structure. We observe the persistence trend between sequences of base pairs, which indicates long-range correlations between base pairs. We also identified the stochastic nature of the DNA sequences of both species.

Detection of Gate Valve Leaks through the Analysis Fractal Characteristics of Acoustic Signal

This paper considers the possibility of using monofractal and multifractal analysis of acoustic signals to detect water leaks through gate valves. Detrended fluctuation analysis (DFA) and multifractal detrended fluctuation analysis (MF-DFA) were used. Experimental studies were conducted on a ½-inch nominal diameter wedge valve, which was fitted to a ¾-inch nominal diameter steel pipeline. The water leak was simulated by opening the valve. The resulting leakage rates for different valve opening conditions were 5.3, 10.5, 14, 16.8, and 20 L per minute (L/min). The Hurst exponent for acoustic signals in a hermetically sealed valve is at the same level as a deterministic signal, while the width of the multifractal spectrum closely matches that of a monofractal process. When a leak occurs, turbulent flow pulsations appear, and with small leak sizes, the acoustic signals become anticorrelated with a high degree of multifractality. As the leakage increases, the Hurst exponent also increases and the width of the multifractal spectrum decreases. The main contributor to the multifractal structure of leak signals is small, noise-like fluctuations. The analysis of acoustic signals using the DFA and MF-DFA methods enables determining the extent of water leakage through a non-sealed gate valve. The results of the experimental studies are in agreement with the numerical simulations. Using the Ansys Fluent software (v. 19.2), the frequencies of flow vortices at different positions of gate valve were calculated. The k-ω SST turbulence model was employed for calculations. The calculations were conducted in a transient formulation of the problem. It was found that as the leakage decreases, the areas with a higher turbulence eddy frequency increase. An increase in the frequency of turbulent fluctuations leads to enhanced energy dissipation. Some of the energy from ordered processes is converted into the energy of disordered processes.

The effect analysis of shape design of different charging piles based on Human physiological characteristics using the MF-DFA

With the rapid development of new energy vehicles, the users have an increasing demand for charging piles. It is generally believed that the charging pile is a kind of practical product, and it only needs to realize the charging function. However, as a product, the shape design of the charging pile will directly affect the user experience, thus affecting product sales. Therefore, in the face of increasingly fierce market competition, when designing the shape of charging piles, it is necessary to adopt the traditional evaluation method and human physiological cognitive characteristics to evaluate the shape of charging piles more objectively. From the user’s point of view, using the electroencephalogram (EEG) of the user, with the help of the multifractal detrended fluctuation analysis (MF-DFA) method, this paper comprehensively analyzes the differences in emotional cognitive characteristics between two kinds of charging piles, namely, the charging pile with a curved appearance design and the charging pile with square appearance design. The results show that there are significant differences in human physiological cognitive characteristics between two kinds of charging piles with different shapes. And different shapes of charging piles have different physiological cognitive differences for users. When designing charging pile product shapes, human beings can objectively evaluate the product shape design according to the physiological cognition differences of users, so as to optimize the charging pile product shape design.

Detection of Pipeline Leaks Using Fractal Analysis of Acoustic Signals

In this paper, the possibility of using monofractal and multifractal analysis of acoustic signals of pipelines to detect leaks is considered. An experimental stand has been created to study the fractal characteristics of acoustic signals of pipelines with “slit” type defects. During the experiments, defects of the “slit” type pipeline with dimensions of 2 mm, 8 mm, and 20 mm were modeled. Detrended fluctuation analysis (DFA) and the multifractal detrended fluctuation analysis (MF-DFA) were used. As a result of the experimental studies, it was found that the occurrence of leakage leads to the occurrence of anticorrelated vibrations in a pipeline with multifractal properties. The analyses of acoustic signals by DFA and MF-DFA methods make it possible to reliably determine the leakage. The Hurst exponent and the width of the multifractal spectrum can serve as indicators of the occurrence of leaks in pipelines.

Determination of local fractal dimension of the catalyst support MgAl2O4 surface

In this paper, a procedure for estimating local fractal dimensionality values for greyscale images was developed. This procedure was tested on synthesised fractal and multifractal Brownian surfaces. The use of the method of detrended fluctuation analysis to determine the Hurst index for samples with a size not exceeding 2000 points was analysed. The optimal values of the sample size and the scale parameter have been obtained, allowing the Hurst index to be calculated with an error of less than 20%. The procedure was also tested on greyscale images, which are 8-bit representations of a synthesised fractal surface. The peculiarities of the application of the procedure for calculating the local fractal dimension for images obtained by scanning electron microscopy have been analysed. The values of the local fractal dimension of the oxide support MgAl2O4 are calculated using SEM images at different magnifications. It has been shown that, taking into account the fractal dimensionality calculation, different morphologies of the particle surface are observed at different scales of image magnification. At the highest magnification, the particle surface is found to consist of embedded smooth micron particles. The surface morphology of the MgAl2O4 particle depends on the micro- and mesopores between the embedded particles, this surface can be characterised by a fractal surface with FD2 = 2.3–2.4.

Detection of long-range correlation causing multifractality in H time series of geomagnetic field over the Northern Hemisphere during quiet geomagnetic conditions

The generation of geomagnetic time series frequently involves intricate spatio-temporal dynamics, wherein nonlinearity and scaling emerge as pivotal mechanisms. The present work investigates the fractal properties of geomagnetic field, and its sources during quiet geomagnetic conditions, by analyzing the horizontal component data of 1 min resolution (H time series) from different latitude regions. Analysis using Auto Correlation Function (ACF), Power spectrum analysis (PSA), Rescaled range analysis (R/S) and Detrended Fluctuation Analysis (DFA) gave indications of the presence of long-range correlations, fractal properties and scaling behaviour of quiet period H time series data. The strong q dependence of generalized Hurst exponent h(q) and scaling exponent Ʈ(q), obtained from the Multifractal Detrended Fluctuation Analysis (MFDFA) method, confirmed the multifractal behaviour of quiet period H time series. The multifractal source analysis of the quiet period H time series with its shuffled and surrogate time series data revealed that, the multifractal characteristics are caused almost entirely by the long-range correlations between small and large fluctuations. The analysis of the latitudinal variations in the multifractal characteristics is also performed as a part of the work, by considering H time series belonging to various latitudes under almost same longitude. The observed decrease in the generalized Hurst exponent values with increase in latitude indicates the change in the multifractal characteristics of the time series with latitude. Also the work revealed that, the H time series from high latitude region shows anti-persistent behaviour, even when the H time series from observatories located at the low and mid latitude regions exhibiting persistent behaviour. The change in the persistence, anti-persistence behaviour can be related to the strength of Earth’s magnetic field.

Surge prediction in a gas-liquid mixed-flow pump based on multifractal detrended fluctuation analysis

Surge causes a sudden drop in pressure increase and possibly results in severe vibration in a multiphase pump once inlet gas volume fraction (IGVF) exceeds a critical value. In this study, a synchronous test system including a high-speed camera, a laser Doppler vibrometer and high-frequency pressure fluctuation sensors is constructed to measure shaft vibration and pressure fluctuation in a gas–liquid mixed-flow pump at different IGVFs. The multifractal characteristics of the collected signals obtained by using the multifractal detrended fluctuation analysis method have been analysed and compared in detail. Results show that pressure surge occurs once the flow pattern transforms from bubbly flow to gas pocket flow in the pump. The multifractal characteristics of the vibration and pressure fluctuations depend strongly on the IGVF. Before the surge, the multifractal strength of vibration and pressure fluctuation increase with the increment of IGVF. After the surge, they decrease rapidly as the bubble coalescence into a mass of gas pockets. Furthermore, the local fluctuation of the vibration is insensitive to the variation of the IGVF and the multifractal spectrum has a right tail at each IGVF. The local fluctuation of the pressure fluctuation become severe with the coalescence of bubbles and the multifractal spectrum has a left tail after the surge. The incipient surge state can be effectively predicted by characteristics parameters extracted from the multifractal spectrum of the shaft vibration and the pressure fluctuation in the pump. This study provides an effective method for surge state prediction in multiphase pumps.

Unraveling the Seismic Signal Anomaly at Mount Rinjani Station: In-Depth Exploration with the Detrended Fluctuation (DFA) Analysis Method in Connection with the 2018 Big Earthquake on Lombok Island, West Nusa Tenggara

We analyzed the seismic signals of the Mount Rinjani station to identify possible seismic anomalies before a series of major earthquakes on Lombok Island in 2018. We observe anomalies before earthquake events Mw &gt;= 5.90. This research applies the detrended fluctuation analysis (DFA) method to investigate possible earthquake precursors associated with the analyzed earthquake. The results showed a relationship between scaling seismic signals (α) that exceeds the threshold of α values during the analysis period, and there is a deviation of the root mean square fluctuations in the corresponding scaling that should be rising but constant. The value of α with constant root mean square fluctuations occurs one to three days before the preliminary earthquake Mw 6.40 (28/07/2018) UTC and eight to 10 days before the main earthquake Mw 6.90 (05/08/2018). The Mw 6.90 earthquake had the most magnitude and could significantly contribute to the appearance of seismic anomalies.

Determination of duration, threshold and spatiotemporal distribution of extreme continuous precipitation in nine major river basins in China

China is one of the countries most severely affected by extreme precipitation, and it is urgent to carry out relevant research on the spatiotemporal distribution of extreme precipitation in China. Compared with single-day precipitation events, heavy precipitation events often last for multiple days and have greater potential disaster impacts, such as floods and mudslides. Therefore, in this study, we focus on continuous precipitation (CP) events for analysis. In order to determine the most probable duration of continuous heavy precipitation events, we innovatively adopted two time-frequency variation methods, namely Fast Fourier Transform (FFT) and Continuous Wavelet Transform (CWT). Then through Detrended Fluctuation Analysis (DFA) and multifractal DFA (MF-DFA) methods, extreme CP thresholds are extracted according to the fluctuation characteristics of the CP series. The results show that the average duration of heavy precipitation in the Pearl River Basin (PRB) area was the longest (up to 7.7 days), followed by the Continental Basin (CB) area (7.6 days). The Haihe River Basin (HRB) area had the shortest duration of heavy precipitation (5.0 days), followed by the Huaihe River Basin (HURB) area (5.9 days). The extreme CP threshold in the Southeast Basin (SEB) area was the largest (112.17 mm), followed by the PRB area (108.22 mm). The extreme CP threshold in the CB area was the smallest (20.17 mm), followed by the Yellow River Basin (YRB) area (44.31 mm). Through mutation and trend testing to evaluate the changing state of the extreme CP time series, it was found that, with one exception (HRB), the average extreme CP after the mutation in the watershed areas was larger than that before the mutation, and eight watersheds showed an upward trend in extreme CP. This suggests that most watershed areas in China are at risk of extreme CP increases. This study can provide an important reference for the analysis of extreme CP in China.

Cavitation identification in a hydraulic bulb turbine based on vibration and pressure fluctuation measurements

Cavitation can lead to reduced efficiency, increased vibration and noise in hydraulic turbines. Accurate and rapid identification of cavitation states in a turbine is important. In this work, a test system has been constructed for a hydraulic bulb turbine, to synchronously obtain cavitation images on runner blades, vibrations on both the runner hub and the runner chamber, and pressure fluctuations on the draft tube of the turbine at different cavitation conditions. The multifractal characteristics of the collected signals obtained by using the multifractal detrended fluctuation analysis method have been analysed and compared in detail. It is found that the multifractal characteristics of the vibrations and pressure fluctuations depend strongly on the cavitation state. The multifractal strength of the pressure fluctuations in the draft tube is stronger than that of the vibrations on the runner, induced by cavitation. Furthermore, some multifractal parameters of vibrations and pressure fluctuations have been extracted and used for cavitation state identification in the turbine, which is important for safe operation of a turbine.

Scaling Exponents of Time Series Data: A Machine Learning Approach.

In this study, we present a novel approach to estimating the Hurst exponent of time series data using a variety of machine learning algorithms. The Hurst exponent is a crucial parameter in characterizing long-range dependence in time series, and traditional methods such as Rescaled Range (R/S) analysis and Detrended Fluctuation Analysis (DFA) have been widely used for its estimation. However, these methods have certain limitations, which we sought to address by modifying the R/S approach to distinguish between fractional Lévy and fractional Brownian motion, and by demonstrating the inadequacy of DFA and similar methods for data that resembles fractional Lévy motion. This inspired us to utilize machine learning techniques to improve the estimation process. In an unprecedented step, we train various machine learning models, including LightGBM, MLP, and AdaBoost, on synthetic data generated from random walks, namely fractional Brownian motion and fractional Lévy motion, where the ground truth Hurst exponent is known. This means that we can initialize and create these stochastic processes with a scaling Hurst/scaling exponent, which is then used as the ground truth for training. Furthermore, we perform the continuous estimation of the scaling exponent directly from the time series, without resorting to the calculation of the power spectrum or other sophisticated preprocessing steps, as done in past approaches. Our experiments reveal that the machine learning-based estimators outperform traditional R/S analysis and DFA methods in estimating the Hurst exponent, particularly for data akin to fractional Lévy motion. Validating our approach on real-world financial data, we observe a divergence between the estimated Hurst/scaling exponents and results reported in the literature. Nevertheless, the confirmation provided by known ground truths reinforces the superiority of our approach in terms of accuracy. This work highlights the potential of machine learning algorithms for accurately estimating the Hurst exponent, paving new paths for time series analysis. By marrying traditional finance methods with the capabilities of machine learning, our study provides a novel contribution towards the future of time series data analysis.

South Africa's Public Debt: Long-term Dependence, Structural Breaks and Multifractality

This paper aims to analyse the evolution of public debt in South Africa using new and original methods. The case of South Africa has been little studied in the literature on debt because the level of debt in this country remains reasonable. Moreover, the use of non-standard methods allows for a fine-grained analysis of the public debt time series and, consequently, to draw unprecedented conclusions. Using the Multifractal Detrended Fluctuation Analysis (MF-DFA) method borrowed from solid state physics and medicine, we conclude that South Africa's debt has a multifractal character, which originates from the long memory effect. Thus, South Africa's public debt is unsustainable. The inefficiency of this market has been particularly exacerbated by the various shocks throughout the sample period.

Regional Multifractal Variability of the Overall Seismic Activity in Pakistan from 1820 to 2020 via the Application of MDFA on Earthquake Catalogs

The overall seismicity of Pakistan from 1820 to 2020 is analysed in terms of its multifractal behaviour. Seismic events of magnitude ML = 3.0 and above are spatially clustered into four distinct groups, each one corresponding to a different region of high seismic activity. The Multifractal Detrended Fluctuation Analysis (MFDA) method applied on each cluster reveals pronounced inter-cluster heterogeneity in terms of the resulting generalised Hurst exponent and fractality spectrum, possibly due to the particular tectonic characteristics of the regions under investigation. Additional results on the variability of the Gutenberg–Richter b-value across the defined clusters further corroborate the uniqueness of the seismic profile of each region.

Santa Ana Winds: Multifractal Measures and Singularity Spectrum

A multifractal analysis based on the time series of temperature, pressure, relative humidity, wind speed, and wind direction was performed for 16 weather stations located in the hydrographic basin of the Guadalupe River in Baja California, Mexico. Our analysis included a 38-year dataset from MERRA-2 database, we investigated the multifractal nature of daily time series data for climatic variables associated with the Santa Ana Winds. We employed the Multifractal Detrended Fluctuation Analysis (MFDFA) method to extract multifractal complexity parameters (α0, ∆α, and r). This was adequate to evaluate the multifractality of the time series that represented the conditions of the phenomenon’s occurrence. From the estimation of the generalized Hurst exponent (hq), it was possible to characterize the time series of the meteorological variables in terms of the characteristics of persistence, anti-persistence, or randomness. Finally, the values corresponding to the parameters and characteristics of the multifractal spectrum or singularities can be used as quantitative and qualitative indicators to describe the dynamics of meteorological processes during the occurrence of the Santa Ana winds in the Guadalupe basin.

Multifractal Characteristics of Smooth Blasting Overbreak in Extra-Long Hard Rock Tunnel

With the development of infrastructure construction in mountainous areas, the number of new extra-long tunnels is increasing. However, these tunnels often face the challenge of complex and variable surrounding rock grades, resulting in a large number of overbreak and underbreak due to the untimely adjustment of smooth blasting parameters. This study focuses on the optimization of the peripheral hole charging structure and blasting parameters for extra-long hard rock tunnels, aiming to improve the effectiveness of smooth blasting technology. The results of this study demonstrate a significant improvement in the effect of smooth blasting after implementing bidirectional polymerization blasting in the tunnel. A comparison between the bidirectional shaped charge and spaced decoupled charge blasting reveals that the former yields better results. To obtain accurate data on the tunnel section profile during excavation, a laser cross-section meter is used for measurement. Furthermore, this study quantitatively compares the optimization effect of smooth blasting parameters. The multifractal characteristics of the tunnel profile overbreak point sequences are analyzed under different smooth blasting schemes using the multifractal detrended fluctuation analysis (MF-DFA) method. It is found that both the spaced decoupled charge and the bidirectional shaped charge blasting exhibit multifractal features in the overbreak measurement point sequences. The calculation results of the multifractal features of the tunnel profile under different smooth blasting plans are in line with the actual situation.

Multifractal analysis of the Southern Oscillation Index

In this paper, multifractal properties of the Southern Oscillation Index (SOI) have been analyzed using Empirical Mode Decomposition (EMD) and Multifractal Detrended Fluctuation Analysis (MFDFA) for the time interval between 1991 to 2020. The joint application of the EMD and detrended fluctuation analysis methods allowed the signal to be separated into three subsets, each with different scaling properties. Then each of these subsequences was analyzed using the MFDFA.Results show that a different multifractality structure characterizes each subset. We observe the strongest multifractality in the macroscale component followed by the medium-scale subsequence. The microscale has the lowest multifractality of the three. The removal of temporal correlations by shuffling the sequences showed that the leading cause of multifractality is the different long-range correlations for small and large fluctuations.

Are clean energy markets efficient? A multifractal scaling and herding behavior analysis of clean and renewable energy markets before and during the COVID19 pandemic

The literature lacks thorough and adequate evidence of the efficiency and herding behavior of clean and renewable energy markets. Therefore, the key objective of this paper is to explore the multifractality and efficiency of six clean energy markets by applying a robust method of Multifractal detrended fluctuation analysis (MFDFA) on daily data over a lengthy period. In addition, to examine the inner dynamics of clean energy markets around the global pandemic (COVID19), the data are further divided into two sub-periods of before and during COVID19. Our sampled clean energy markets exhibit multifractal behavior with a significant impact on the efficiency and intensified presence of multifractality during the COVID19 period. Overall, TXCT and BSEGRNX were the most efficient clean energy markets, but the ranking of TXCT deteriorated significantly in the sub-periods. The presence of multifractality and herding behavior symmetry intensified during the crisis period, which gives a potential for advancing portfolio management techniques. Moreover, our study provides practical implications and new insights for various market participants for better management and understanding of risks.

Abstract 16676: Risk Assesment of Sudden Cardiac Death With RR Interval Fluctuations

Introduction: Changes in conventional measures for short-term heart rate variability (HRV) have been associated with heart failure, coronary artery disease and even sudden cardiac death (SCD). However, the predictive value of HRV in clinical settings has been limited. Secondly, the current HRV methods have not discriminated SCDs from other causes of death, which would be relevant for proper prevention and treatment. In this study we utilize novel time series analysis methods for RR intervals in ultra-short-term measurements to distinguish SCD from other causes of death. Methods: We apply second-order detrended fluctuation analysis (DFA) with maximally overlapping windows to assess the correlations in RR intervals as a function of the scale, i.e., the range of consecutive RR intervals in one-minute resting ECG. The analysis is based on the baseline ECG recordings from the prospective FINCAVAS study of cardiac patients with a median follow-up time of 8.3 years, during which 378 deaths were recorded including 76 SCDs in the total population of 2794 subjects. Results: Our DFA method can discriminate between incident SCD cases and patients dying to other causes. The discrimination is maximized on scale 9, with an univariate hazard ratio of 0.71 and 95% confidence intervals (CI) (0.55-0.91). Excluding other cardiac deaths from the control group we are left with 279 deaths resulting to univariate hazard ratio of 0.62 (0.47-0.82 CI) on scale 8. Conclusions: The ability to distinguish SCD from other causes of death shows that the scale-dependent DFA method is a superior alternative to the conventional HRV methods. The utilization of one-minute RR interval measurements for risk assessment provides new non-invasive tools for clinical inspections, as well as promising prospects to health monitoring with wearable devices.