Detrended Fluctuation Analysis 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

IntroductionSleep-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.MethodsThe 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.ResultsCompared 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.ConclusionThis 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.

Extreme Events Cause Market Efficiency or Inefficiency? Evidence from Precious Metals and Green Stock Indices

Background: Green investments offer a promising market-based approach to tackling global climate change but are susceptible to risk transmission from multiple assets. Purpose: To examine the multifractality between precious metals (Gold, Silver, Platinum) and green stock indices, such as Clean Energy Fuels, Nasdaq Clean Edge Green Energy, S&P Global Clean Energy and WilderHill Clean Energy, over the period from 1 January 2018 to 23 November 2023. The study aims to answer the following question: Did the events of 2020 and 2022 cause efficiency or inefficiency in the markets analysed? Methods: The Detrended Fluctuation Analysis (DFA) econophysics model will be used to answer the research question. Results: During the period of stability, there was a clear division between the markets, with Gold and green energy indices demonstrating market efficiency, while Platinum, Silver and some green indices exhibited price persistence, suggesting opportunities for above-average gains. However, the 2020 global pandemic led to widespread inefficiencies in all the markets analysed, with precious metals and green energy indices showing price persistence, indicating patterns that could lead to arbitrage opportunities. The persistence in returns suggested a tendency for asset prices to continue in the same direction for an extended period, offering opportunities to identify ongoing market trends for investment. In the pre-conflict period, the random walk hypothesis was rejected in all markets, with precious metals exhibiting anti-persistence in returns, while green energy indices showed significant persistence. During the conflict period, precious metals and green energy indices converged towards persistence in returns, except Platinum, which showed anti-persistence. Conclusion: This study provides valuable insights for investors and financial market professionals, highlighting the importance of understanding asset price behaviour patterns in different economic contexts.

Stock Market Efficiency of the BRICS Countries Pre-, During, and Post Covid-19 Pandemic: A Multifractal Detrended Fluctuation Analysis

Stock Market Efficiency of the BRICS Countries Pre-, During, and Post Covid-19 Pandemic: A Multifractal Detrended Fluctuation Analysis

Improved extended empirical wavelet transform for accurate multivariate oscillation detection and characterisation in plant-wide industrial control loops

The conventional extended empirical wavelet transform (EEWT) proposed recently is intended to decompose multivariate signals with clear peaks in power spectra without considering the cases where the signals contain high noise levels. Even when dealing with signals with distinct peaks, the EEWT method can still encounter challenges in properly decomposing the signals. However, plant-wide data from industrial control loops, including controllers’ outputs, process variables, and manipulated variables, are commonly corrupted by high levels of noise, which can be introduced at various stages of data acquisition, transmission, and processing within the control system. To address these limitations and ensure the applicability of the EEWT to real-world industrial data with diverse and challenging characteristics, this paper presents an improved version called the improved extended empirical wavelet transform (IEEWT). The IEEWT incorporates noise-reduced power spectra and detrended fluctuation analysis techniques to enhance the decomposition. The proposed method demonstrates accurate multivariate data decomposition for both simulated and real data sets, surpassing the limitations associated with the conventional EEWT.

Multifractal fluctuations in zebrafish (Danio rerio) polarization time series.

In this work, we study the polarization time series obtained from experimental observation of a group of zebrafish (Danio rerio) confined in a circular tank. The complex dynamics of the individual trajectory evolution lead to the appearance of multiple characteristic scales. Employing the Multifractal Detrended Fluctuation Analysis (MF-DFA), we found distinct behaviors according to the parameters used. The polarization time series are multifractal at low fish densities and their average scales with . On the other hand, they tend to be monofractal, and their average scales with for high fish densities. These two regimes overlap at critical density , suggesting the existence of a phase transition separating them. We also observed that for low densities, the polarization velocity shows a non-Gaussian behavior with heavy tails associated with long-range correlation and becomes Gaussian for high densities, presenting an uncorrelated regime.

Multifractal detrended fluctuation analysis approach to the monthly total ozone concentration over New Delhi, India

Multifractal detrended fluctuation analysis approach to the monthly total ozone concentration over New Delhi, India

Unravelling the Fractal Complexity of Temperature Datasets across Indian Mainland

Studying atmospheric temperature characteristics is crucial under climate change, as it helps us to understand the changing patterns in temperature that have significant implications for the environment, ecosystems, and human well-being. This study presents the comprehensive analysis of the spatiotemporal variability of scaling behavior of daily temperature series across the whole Indian mainland, using a Multifractal Detrended Fluctuation Analysis (MFDFA). The analysis considered 1° × 1° datasets of maximum temperature (Tmax), minimum temperature (Tmin), mean temperature (Tmean), and diurnal temperature range (DTR) (TDTR = Tmax − Tmin) from 1951 to 2016 to compare their scaling behavior for the first time. Our results indicate that the Tmin series exhibits the highest persistence (with the Hurst exponent ranging from 0.849 to unity, and a mean of 0.971), and all four-temperature series display long-term persistence and multifractal characteristics. The variability of the multifractal characteristics is less significant in North–Central India, while it is highest along the western coast of India. Moreover, the assessment of multifractal characteristics of different temperature series during the pre- and post-1976–1977 period of the Pacific climate shift reveals a notable decrease in multifractal strength and persistence in the post-1976–1977 series across all regions. Moreover, for the detection of climate change and its dominant driver, we propose a new rolling window multifractal (RWM) framework by evaluating the temporal evolution of the spectral exponents and the Hurst exponent. This study successfully captured the regime shifts during the periods of 1976–1977 and 1997–1998. Interestingly, the earlier climatic shift primarily mitigated the persistence of the Tmax series, whereas the latter shift significantly influenced the persistence of the Tmean series in the majority of temperature-homogeneous regions in India.

A novel approach for cardiac pathology detection using phonocardiogram signal multifractal detrended fluctuation analysis and support vector machine classification

A novel approach for cardiac pathology detection using phonocardiogram signal multifractal detrended fluctuation analysis and support vector machine classification

Understanding the Efficiency Levels among Cryptocurrencies: Islamic, Green and Traditional

Background: Islamic cryptocurrencies are different from conventional ones in that they are backed by physical assets and are based on religious principles. After the COVID-19 pandemic, cryptocurrencies showed different behavior. However, there are not many studies on the efficiency, in its weak form, of these three typical families of cryptocurrencies (Islamic, green, and traditional). Purpose: This study compares the efficiency levels of Islamic cryptocurrencies (HelloGold), green cryptocurrencies (Cardano, NANO, Stellar, IOTA), and traditional cryptocurrencies (BTC and ETH) in the preceding period and during the geopolitical conflict between Russia and Ukraine in 2022. Methods: This research will use Lo and Mackinlay's (1988) variance ratio methodology, and the Detrended Fluctuation Analysis (DFA) model will be used. Results: The results indicate that the Islamic currency HGT and the green currency XNO display significant information asymmetries, rejecting the random walk hypothesis for various time intervals. Similarly, other green currencies such as XLM, ADA, and MIOTA, as well as ETH and BTC, reject the hypothesis to varying degrees and time intervals. Furthermore, the Islamic cryptocurrency (HelloGold) was anti-persistent before and during the conflict. The digital currencies ADA and BTC are persistent in both periods. ETH is in equilibrium in the pre-conflict period and becomes persistent during the conflict (0.50 - 0.56), while MIOTA and XLM are persistent during the pre-conflict period and shift to equilibrium during the Russian invasion of Ukraine in 2022. Finally, the XNO eco-currency shows the same anti-persistence characteristics during the two sub-periods. Conclusion: These results highlight the complexity and dynamics of cryptocurrency markets, indicating that different digital currencies can exhibit different temporal behaviors regarding information efficiency and persistence or anti-persistence patterns.

Multifractal analysis of Chinese literary and web novels

Multifractal analysis of literary works, utilizing measures such as sentence length and word length as time series, have revealed the prevalence of multifractal structures within these works. After constructing a corpus of 712 Chinese novels, we performed multifractal detrended fluctuation analysis (MF-DFA) and multifractal detrending moving average analysis (MF-DMA) on them. Both method revealed that non-monotonic generalized Hurst exponential curves and distorted spectral functions appeared in about half of the web novels, but were rarely found in literary novels. By conducting a meticulous examination of sentence length sequences and adjustment of the time series range covered by the computation, it becomes apparent that this irregular Hurst exponent curve stems from the uneven distribution of long sentences within the work. This uneven distribution mirrors the instability present in the author’s creative style, which is intimately linked to the characteristics of the publishing mechanisms for web novels.

Multivariate Detrended Fluctuation Analysis of Symbolic Sequences

Sequences formed by symbols are found in diverse fields, including genome sequences, written texts and computer codes. An interesting question is whether a sequence of symbols contains correlated structures. Existing methods to characterize correlations require a numerical representation of the sequence. In this regard, mapping a sequence of text into a sequence of numerical values is a key step for assessing correlation analysis. This work proposes a methodology to study correlations in a sequence of symbols. In the first step, the sequence of symbols is mapped in a multivariate numerical sequence formed by unit vectors in a vectorial space. The main feature of such mapping is that symbols are equally weighted, thus avoiding the numerical overrepresentation of symbols. In the second step, a multivariate version of the detrended fluctuation analysis is used to quantify correlations in the numerical sequence. Genome sequences (first COVID-19), written English texts and comovements between Bitcoin and gold markets were used to illustrate the proposed methodology’s performance. The results showed that the balanced numerical mapping of symbolic sequences and the multivariate DFA provides valuable insights into the correlations in a sequence of symbols.

Characterizing the Solar Cycle Variability Using Nonlinear Time Series Analysis at Different Amounts of Dynamo Supercriticality: Solar Dynamo is Not Highly Supercritical

The solar dynamo is essentially a cyclic process in which the toroidal component of the magnetic field is converted into the poloidal one and vice versa. This cyclic loop is disturbed by some nonlinear and stochastic processes mainly operating in the toroidal to poloidal part. Hence, the memory of the polar field decreases in every cycle. On the other hand, the dynamo efficiency and, thus, the supercriticality of the dynamo decreases with the Sun’s age. Previous studies have shown that the memory of the polar magnetic field decreases with the increase of supercriticality of the dynamo. In this study, we employ popular techniques of time series analysis, namely, compute Higuchi’s fractal dimension, Hurst exponent, and Multi-Fractal Detrended Fluctuation Analysis to the amplitude of the solar magnetic cycle obtained from dynamo models operating at near-critical and supercritical regimes. We show that the magnetic field in the near-critical regime is governed by strong memory, less stochasticity, intermittency, and breakdown of self-similarity. On the contrary, the magnetic field in the supercritical region has less memory, strong stochasticity, and shows a good amount of self-similarity. Finally, applying the same time series analysis techniques in the reconstructed sunspot data of 85 cycles and comparing their results with that from models, we conclude that the solar dynamo is possibly operating near the critical regime and not too much supercritical regime. Thus the Sun may not be too far from the critical dynamo transition.

Evaluation of the optimal number of steps to obtain reliable running spatio-temporal parameters and their variability

BackgroundSpatio-temporal running parameters and their variability help to determine a runner's running style. However, determining whether a change is due to the measurement or to a specific condition such as an injury is a matter of debate, as no recommendation on the number of steps required to obtain reliable assessments exists. Research questionWhat is the optimal number of steps required to measure different spatio-temporal parameters and study their variability at different running speeds? MethodsTwenty-five runners performed three experimental sessions of three bouts of treadmill running at 8, 10 and 12 km/h separated by 24 h. We measured cadence, stride, step, contact and flight time. We calculated the duty factor and the leg stiffness index (Kleg). Mean spatio-temporal parameters and linear (coefficient of variation, standard deviation) and non-linear (Higuchi fractal index, α1 coefficient of detrended fluctuation analysis) analyses were computed for different numbers of steps. Relative reliability was determined using the intraclass coefficient correlation. The minimal number of steps which present a good reliability level was considered as the optimal number of steps for measurement. Absolute reliability was assessed by calculating minimal detectable change. ResultsTo assess the mean values of spatio-temporal running parameters, between 16 and 150 steps were required. We were unable to obtain an optimal number of steps for cadence, stride and step-time variabilities for all speeds. For the linear analyses, we deduced the optimal number of steps for Kleg and the contact time (around 350 steps). Non-linear analyses measurements required between 350 and 540 steps, depending on the parameter. SignificanceResearchers and clinicians should optimize experimental conditions (number of steps and running speed) depending on the parameter or the variability analysis targeted. Future studies must use absolute reliability metrics to report changes in response to a specific condition with no bias due to measurement error.

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.

EEG complexity measures for detecting mind wandering during video-based learning

This study explores the efficacy of various EEG complexity measures in detecting mind wandering during video-based learning. Employing a modified probe-caught method, we recorded EEG data from participants engaged in viewing educational videos and subsequently focused on the discrimination between mind wandering (MW) and non-MW states. We systematically investigated various EEG complexity metrics, including metrics that reflect a system’s regularity like multiscale permutation entropy (MPE), and metrics that reflect a system’s dimensionality like detrended fluctuation analysis (DFA). We also compare these features to traditional band power (BP) features. Data augmentation methods and feature selection were applied to optimize detection accuracy. Results show BP features excelled (mean area under the receiver operating characteristic curve (AUC) 0.646) in datasets without eye-movement artifacts, while MPE showed similar performance (mean AUC 0.639) without requiring removal of eye-movement artifacts. Combining all kinds of features improved decoding performance to 0.66 mean AUC. Our findings demonstrate the potential of these complexity metrics in EEG analysis for mind wandering detection, highlighting their practical implications in educational contexts.

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.

Fluctuation Analysis of Uterine Contractions in Term Pregnancies Using Electrohysterography Signals and Empirical Mode Decomposition-Based Multifractal Features

Investigating the fluctuations of uterine contractions is an indispensable diagnostic practice to evaluate the onset of labor. This work aims to differentiate the fluctuations associated with Term (gestation ≥ 37 weeks) pregnancies during varied gestational ages using electrohysterography (EHG) signals. The signals in the second and third trimesters are subjected to Multifractal-Empirical Mode Decomposition-based Detrended Fluctuation Analysis (MF-EMDDFA). Multifractal spectrum is estimated and features namely, Holder exponents ([Formula: see text], [Formula: see text]), broadness (BD), root slopes (LS, RS) and tangential slopes (TL, TR) are extracted. Machine learning methods, such as Naïve Bayes, adaptive boosting and random forest (RF) classifiers, are utilized to discriminate the contractions during different weeks of gestation. Results show that five multifractal features, namely [Formula: see text], [Formula: see text], BD, LS and TL, show significant differences between the considered gestational ages. An increase in regularity of the uterine contractions is observed as the gestational age increases. These features along with the RF classifier provide an accuracy, sensitivity, precision, recall and F1-score of greater than 98.30%. As the differentiation of uterine contractions during different weeks of gestation is vital to understanding the pregnancy progress, the proposed multifractal features could be used as potential biomarkers in clinical practices.