Hurst Exponent Values Research Articles

INTEGRATED MODEL FOR FORECASTING TIME SERIES OF ENVIRONMENTAL POLLUTION PARAMETERS

The quality of life in large urban areas is considerably diminished by air pollution, with major contributors being motor vehicles, industrial activities, and fossil fuel combustion. A major contributor to air pollution is coal-fired and thermal power plants, which are commonly found in emerging markets. In Astana, Kazakhstan, a rapidly expanding city's significant reliance on coal for heating and considerable building exacerbate air pollution. This research is essential for improving urban development practices that support sustainable growth in rapidly expanding cities. Using time series data from four monitoring stations in Astana using fractal R/S analysis, the study looks at long-term patterns in air pollutant levels, especially PM10 and PM2.5. The stations' Hurst exponents were determined to be 0.723, 0.548, 0.442, and 0.462. Additionally, the flow window method was used to study the Hurst exponent's dynamic behavior. The findings showed that one station's pollution levels had long-term memory, which suggests that the time series is persistent. While anti-persistence was noted in the third and fourth sites, data from the second station indicated nearly random behavior. The Hurst exponent values explain the October 2021 spike in pollution levels, which is probably caused by thermal power plants close to the city. The fractal analysis of time series could serve as an indicator of environmental conditions in a given region, with persistent pollution trends potentially aiding in predicting critical pollution events. Anti-persistence or temporary pollution spikes may be influenced by the observation station's proximity to pollution sources. Overall, the findings suggest that fractal time series analysis can act as a valuable tool for monitoring environmental health in urban areas.

Inner Multifractal Dynamics in the Jumps of Cryptocurrency and Forex Markets

Jump dynamics in financial markets exhibit significant complexity, often resulting in increased probabilities of subsequent jumps, akin to earthquake aftershocks. This study aims to understand these complexities within a multifractal framework. To do this, we employed the high-frequency intraday data from six major cryptocurrencies (Bitcoin, Ethereum, Litecoin, Dashcoin, EOS, and Ripple) and six major forex markets (Euro, British pound, Canadian dollar, Australian dollar, Swiss franc, and Japanese yen) between 4 August 2019 and 4 October 2023, at 5 min intervals. We began by extracting daily jumps from realized volatility using a MinRV-based approach and then applying Multifractal Detrended Fluctuation Analysis (MFDFA) to those jumps to explore their multifractal characteristics. The results of the MFDFA—especially the fluctuation function, the varying Hurst exponent, and the Renyi exponent—confirm that all of these jump series exhibit significant multifractal properties. However, the range of the Hurst exponent values indicates that Dashcoin has the highest and Litecoin has the lowest multifractal strength. Moreover, all of the jump series show significant persistent behavior and a positive autocorrelation, indicating a higher probability of a positive/negative jump being followed by another positive/negative jump. Additionally, the findings of rolling-window MFDFA with a window length of 250 days reveal persistent behavior most of the time. These findings are useful for market participants, investors, and policymakers in developing portfolio diversification strategies and making important investment decisions, and they could enhance market efficiency and stability.

Analysis of Tuberculosis (TB) Case Patterns Using the Hurst Exponent Fractal Dimension Method in North Sumatra

Tuberculosis is a chronic infectious disease caused by Mycobacterium tuberculosis. This bacteria is commonly known as Acid Resistant Bacilli (BTA). The Hurst Exponent Fractal Dimension method was used in this work to identify the properties of time series data and fractal patterns in tuberculosis (TB) patients. The Hurst exponent method is calculated by the smallest prime factor that divides the data (pi). This fractal dimension's value is calculated using the Hurst exponent value. Time series data is classified into three groups depending on computation results: random, anti-persistence, and persistence. In the study, three data ranges (n) were obtained from the observed data, namely tuberculosis (TB) patients from July to December 2023 (174, 87, and 29). The value of the Hurst exponent obtained was 0,475 (0<H<0,5) and the value of the fractal dimension obtained was 1,525 (1,5<H<2). Based at the Hurst exponent value and fractal dimension fee, it indicates that the records is anti-persistence. Anti-persistence means that the time series data of cases of tuberculosis (TB) patients which if the data increases at one time, it tends to decrease at the next time and if the data decreases at one time, it tends to increase at the next time.

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.

Space–Time Variations in the Long-Range Dependence of Sea Surface Chlorophyll in the East China Sea and the South China Sea

Gaining insights into the space–time variations in the long-range dependence of sea surface chlorophyll is crucial for the early detection of environmental issues in oceans. To this end, 12 locations were selected along the Yangtze River and Pearl River estuaries, varying in distances from the Chinese coastline. Daily satellite-observed sea surface chlorophyll concentration data at these 12 locations were collected from the Copernicus Marine Service website, spanning from December 1997 to November 2023. The main objective of the current study is to introduce a multi-fractional generalized Cauchy model for calculating the values of Hurst exponents and quantitatively assessing the long-range dependence strength of sea surface chlorophyll at different spatial locations and time instants during the study period. Furthermore, ANOVA was utilized to detect the differences of calculated Hurst exponent values among the locations during various months and seasons. From a spatial perspective, the findings reveal a significantly stronger long-range dependence of sea surface chlorophyll in offshore regions compared to nearshore areas, with Hurst exponent values > 0.5 versus <0.5. It is noteworthy that the values of Hurst exponents at each location exhibit significant differences during various seasons, from a temporal perspective. Specifically, the long-range dependence of sea surface chlorophyll in summer in the nearshore region is weaker than in other seasons, whereas that in the offshore region is stronger than in other seasons. The study concludes that long-range dependence is inversely related to the distance from the coastline, and anthropogenic activity plays a dominant role in shaping the long-range dependence of sea surface chlorophyll in the coastal regions of China.

Mindfulness meditation styles differently modulate source-level MEG microstate dynamics and complexity.

The investigation of mindfulness meditation practice, classically divided into focused attention meditation (FAM), and open monitoring meditation (OMM) styles, has seen a long tradition of theoretical, affective, neurophysiological and clinical studies. In particular, the high temporal resolution of magnetoencephalography (MEG) or electroencephalography (EEG) has been exploited to fill the gap between the personal experience of meditation practice and its neural correlates. Mounting evidence, in fact, shows that human brain activity is highly dynamic, transiting between different brain states (microstates). In this study, we aimed at exploring MEG microstates at source-level during FAM, OMM and in the resting state, as well as the complexity and criticality of dynamic transitions between microstates. Ten right-handed Theravada Buddhist monks with a meditative expertise of minimum 2,265 h participated in the experiment. MEG data were acquired during a randomized block design task (6 min FAM, 6 min OMM, with each meditative block preceded and followed by 3 min resting state). Source reconstruction was performed using eLORETA on individual cortical space, and then parcellated according to the Human Connect Project atlas. Microstate analysis was then applied to parcel level signals in order to derive microstate topographies and indices. In addition, from microstate sequences, the Hurst exponent and the Lempel-Ziv complexity (LZC) were computed. Our results show that the coverage and occurrence of specific microstates are modulated either by being in a meditative state or by performing a specific meditation style. Hurst exponent values in both meditation conditions are reduced with respect to the value observed during rest, LZC shows significant differences between OMM, FAM, and REST, with a progressive increase from REST to FAM to OMM. Importantly, we report changes in brain criticality indices during meditation and between meditation styles, in line with a state-like effect of meditation on cognitive performance. In line with previous reports, we suggest that the change in cognitive state experienced in meditation is paralleled by a shift with respect to critical points in brain dynamics.

Selectivity filter conductance, rectification and fluctuations of subdomains—How can this all relate to the value of Hurst exponent in the dwell-times of ion channels states?

The Hurst effect in the signals describing ion channels’ activity has been known for many years. This effect is present in the experimental recordings of single-channel currents, but not only. The sequences of dwell times of functionally different channel states also exhibit long-range correlations. We have found that the memory effect within the dwell-time series is related to the coupling between the channel’s activation gate (AG) and selectivity filter (SF), which controls the ion conduction. In this work, we analyzed both the experimental data describing the activity of potassium channels of different types (e.g., BK, mitoBK, mitoTASK-3, mitoKv1.3, TREK-2-like channels) and the series generated according to our previously proposed Hurst effect model. The obtained results suggest that the strength of the allosteric cooperation between the AG and SF determines not only the conductance of the channel – which governs how often ions in SF move or remain blocked – but also modulates the correlations present in the dwell times when sampled with a suitably high sampling rate. Moreover, we found that rectification can interfere with this process, contributing to additional changes in correlations within the channel’s sojourns in subsequent states. Similarly, the correlations may be affected by processes proceeding at longer time scales, like interactions with the channel’s auxiliary domains or lipid surroundings.

Methodology and Experimental Protocol for Studying Learning and Motor Control in Neuromuscular Structures in Pilates.

The benefits of Pilates have been extensively researched for their impact on muscular, psychological, and cardiac health, as well as body composition, among other aspects. This study aims to investigate the influence of the Pilates method on the learning process, motor control, and neuromuscular trunk stabilization, specifically in both experienced and inexperienced practitioners. This semi-randomized controlled trial compares the level of experience among 36 Pilates practitioners in terms of motor control and learning of two Pilates-based skills: standing plank and side crisscross. Data will be collected using various assessment methods, including abdominal wall muscle ultrasound (AWMUS), shear wave elastography (SWE), gaze behavior (GA) assessment, electroencephalography (EEG), and video motion. Significant intra- and inter-individual variations are expected, due to the diverse morphological and psychomotor profiles in the sample. The adoption of both linear and non-linear analyses will provide a comprehensive evaluation of how neuromuscular structures evolve over time and space, offering both quantitative and qualitative insights. Non-linear analysis is expected to reveal higher entropy in the expert group compared to non-experts, signifying greater complexity in their motor control. In terms of stability, experts are likely to exhibit higher Lyapunov exponent values, indicating enhanced stability and coordination, along with lower Hurst exponent values. In elastography, experienced practitioners are expected to display higher transversus abdominis (TrA) muscle elasticity, due to their proficiency. Concerning GA, non-experts are expected to demonstrate more saccades, focus on more Areas of Interest (AOIs), and shorter fixation times, as experts are presumed to have more efficient gaze control. In EEG, we anticipate higher theta wave values in the non-expert group compared to the expert group. These expectations draw from similar studies in elastography and correlated research in eye tracking and EEG. They are consistent with the principles of the Pilates Method and other scientific knowledge in related techniques.

Analisis Pola Harga Saham dengan Modifikasi Metode Eksponen Hurst dan Box Counting

A stock chart is a graphical representation of a stock's past performance. The dynamic pattern of stock prices is important to know because an investor wants to invest, expecting high returns with low risk. The dynamic pattern of stock prices can be known by fractal dimension analysis because the stock price graph is self-affine, which is one of the properties of fractal objects. In this study, a modification of the Hurst exponent method and box counting are used to analyze the fractal dimension. The calculated results are classified into three types, namely random, persistent and anti-persistent. Two data intervals are observed, namely January 2018-December 2021 stock prices (48 data) and January 2018-June 2022 stock prices (54 data). The resulting Hurst exponents of the two intervals are 0.043 and 0.003. Based on the resulting Hurst exponent value, the data is anti-persistent because the value 0<H<0.5. Then, the fractal dimension value obtained by applying the box-counting method is 1.547 and 1.562, meaning that Bank Rakyat Indonesia's price pattern is anti-persistent. The meaning of anti-persistent is that in certain months the stock has a high price and in the following months the stock has a low price to be traded.

A modified multifractal detrended fluctuation analysis to study the precipitation across northeast India

Using multifractal detrended fluctuation analysis (MF-DFA), the pre-monsoon rainfall and Indian summer monsoon rainfall (ISMR) from 1871 to 2016 are examined in this work for northeast India. According to observations, rainfall during the pre-monsoon and summer monsoons both exhibit persistence and quasi-randomness. The generalized Hurst Exponent value indicates that the pre-monsoon rainfall time series and the summer monsoon rainfall time series have long-term positive auto-correlation. The fluctuation function obtained through MF-DFA by means of the slopes of ln(Fq(s)) against ln(s) plots is dominated by segments with significant variance, which leads us to believe that the rainfall time series related to the pre- and summer monsoon exhibit multifractal behaviour. The presence of multifractality in the pre- and summer monsoon rainfall time series is further substantiated through the association between the qth-order variance and the length scale.

Modeling venous bias in resting state functional MRI metrics.

Resting-state (rs) functional magnetic resonance imaging (fMRI) is used to detect low-frequency fluctuations in the blood oxygen-level dependent (BOLD) signal across brain regions. Correlations between temporal BOLD signal fluctuations are commonly used to infer functional connectivity. However, because BOLD is based on the dilution of deoxyhemoglobin, it is sensitive to veins of all sizes, and its amplitude is biased by draining veins. These biases affect local BOLD signal location and amplitude, and may also influence BOLD-derived connectivity measures, but the magnitude of this venous bias and its relation to vein size and proximity is unknown. Here, veins were identified using high-resolution quantitative susceptibility maps and utilized in a biophysical model to investigate systematic venous biases on common local rsfMRI-derived measures. Specifically, we studied the impact of vein diameter and distance to veins on the amplitude of low-frequency fluctuations (ALFF), fractional ALFF (fALFF), Hurst exponent (HE), regional homogeneity (ReHo), and eigenvector centrality values in the grey matter. Values were higher across all distances in smaller veins, and decreased with increasing vein diameter. Additionally, rsfMRI values associated with larger veins decrease with increasing distance from the veins. ALFF and ReHo were the most biased by veins, while HE and fALFF exhibited the smallest bias. Across all metrics, the amplitude of the bias was limited in voxel-wise data, confirming that venous structure is not the dominant source of contrast in these rsfMRI metrics. Finally, the models presented can be used to correct this venous bias in rsfMRI metrics.

Exploring vegetation trends and restoration possibilities in Pakistan by using Hurst exponent.

Vegetation cover change and its interaction with climate are significant to study as it has impact on ecosystem stability. We used the Normalized Difference Vegetation Index (NDVI) and climatic factors (temperature and rainfall) for investigating the relationship between vegetation and climate. We also traced spatiotemporal changes in the vegetation in Pakistan from 2000 to 2020; we used the Hurst exponent to estimate future vegetation trends in Pakistan. Our results show an increase in vegetation throughout Pakistan, and the Punjab Province is showing the highest significant vegetation trend at 88.51%. Our findings reveal that the response of vegetation to climate change varies by region and is influenced by local climatic conditions. However, the relationship between rainfall and annual NDVI is stronger than the temperature in the study area-Pakistan. The Hurst exponent value is above 0.5 in all four provinces, that is, the indication of consistent vegetation trends in the future. The highest values are observed in Punjab and Khyber Pakhtunkhwa (KPK). In the Punjab Province, 88.41% of the area showed positive development, with forests in particular showing a significant positive effect on land use classes. On the other hand, the Sindh Province has the highest negative result at 2.87%, with urban areas showing the highest negative development. To sum up, the NDVI pattern and change attribute suggest vegetation restoration in Pakistan.

Fractal dimension used as a proxy to understand the spatial distribution for carlin-type gold deposits

The spatial distribution of ore-forming element grades typically exhibits strong nonlinear characteristics as a result of continuous geological processes. The trend of change in ore grade sequences is a crucial indicator of the degree of enrichment of an ore deposit. Therefore, quantitative evaluation of the spatial distribution of ore-forming elements holds great significance for understanding ore-forming processes as well as for ore exploration. In this work, based on the principles of fractal theory, a MATLAB-based program to calculate fractal dimensions was developed, and fractal analysis was conducted on the gold concentration values (g/t) of 25 drill holes in the Lannigou Gold Mining Area, Guizhou, China. Rescaled range analysis and the fractal correlation integral were utilized to obtain the spatial distribution of gold concentrations in the drill holes. Rescaled range analysis revealed that the Hurst exponent (HR/S) values vary in the range of 0.58–0.97, which reflected the persistent behavior of vertical variation in gold tonnage at the studied wells. Furthermore, the relationship between gold grade distribution and associated fluctuations in the fractal dimension derived from the correlation dimension (DC) was discussed. The DC value was found to vary between 1.01 and 1.59, indicating that high-grade gold deposits were distributed along steep fractal gradients and that fractal dimension values could be used as a reliable proxy to efficiently understand the migration pathways of auriferous fluid. Studies have shown that the Hurst exponent of the Au grade sequence exhibited a strong dependence on the grade of mineralization, with gold mineralized veins persisting throughout the studied drill holes. Thus, fractal dimension gradients can serve as an important proxy for identifying the locations of potential economic gold deposits in unexplored areas. Moreover, this approach can be employed to map the distribution patterns of other types of ore deposits.

Exploring Acute Changes in Hamstring EMG after Warm-up and Stretching Using a Multifractal Analysis.

This study aimed to apply multifractal detrended fluctuation analysis (MFDFA) to surface EMG to detect neuromuscular changes after realistic warm-up procedures that was followed by various stretching exercises. Sixteen volunteers conducted two experimental sessions. Testing included two maximal voluntary contractions before, after a standardized warm-up, and after a stretching exercise (static or neurodynamic nerve gliding technique). EMG was registered on biceps femoris and semitendinosus muscles. EMG was analyzed using different parameters obtained from the singularity Hurst exponent function and multifractal power spectrum (both obtained from the multifractal detrended fluctuation analysis). The Hurst exponent, α maximum, and peak value of the multifractal spectrum significantly decreased after warm-up as compared with baseline for both biceps femoris ( P = 0.003, P = 0.006, and P = 0.003, respectively) and semitendinosus ( P = 0.006, P = 0.013 and P = 0.01, respectively) muscles. No further alteration was obtained after static or neurodynamic nerve gliding stretching as compared with post-warm-up ( P = 1.0). No significant difference was obtained for Hurst exponent range, width, and asymmetry of the multifractal spectrum ( P > 0.05). From the present results, EMG depicted multifractal features sensitive to detect neuromuscular changes after a warm-up procedure. An increase in multiscale complexity is revealed after warm-up without any further alteration after stretching. The multifractal spectrum depicted dominant small fluctuations that shifted toward slightly larger fluctuations that could be attributed to motor unit recruitment.

Fractality in Chinese prose

Abstract This study explores long-range correlations in terms of sentence or segment length variation in Chinese narrative texts and nonfiction prose. (Drożdż et al. 2016, Quantifying origin and character of long-range correlations in narrative texts. Information Sciences, 331 32–44) analyzed Western novels and found fractal patterns, defined as self-similar, wavelet recurrence, and alternation. Inspired by this study, our research tries to determine whether similar patterns commonly exist in Chinese literature and compares the similarities and differences with Western literature. We calculated the Hurst exponent, β-values, and Δα values for ninety-five Chinese novels, ranging historically from late Qing to contemporary Internet novels, covering the geopolitical regions from Mainland China to Taiwan and Hong Kong. We also made comparisons with pre-modern vernacular novels, historical texts in classical Chinese, contemporary nonfiction and expository writings, as well as randomly generated texts. We found that Chinese novels exhibit fractal patterns as well. In particular, the texts exhibit a better fractal quality if the sentence lengths are measured by Chinese characters, instead of words. There is no clear correlation between fractality and cultural–political contexts and individual authors, but historically speaking, modern Chinese texts show stronger long-range correlations than pre-modern texts. Moreover, long-range correlations in Chinese literature are weaker than in Western literature, and there is a lower percentage of novels with multifractal structures. Our data also show that the fractality not only exists in literary texts, but also in nonliterary, non-narrative, and expository writings; yet, there is no long-range correlation in randomly generated texts. We further conclude that fractality is a fundamental feature of prose writing and human writing.

Self-organized criticality in manufacturing system unscheduled downtime series and its application to major failure prediction

In this study, self-organized criticality theory was applied to analyze the unscheduled downtime (USDT) characteristic of a complex manufacturing system. The long-range correlation of the USDT series was verified through the Hurst exponent value. Then, we developed a model to depict the relationship between the frequency and USDT duration with the extreme value theory. The parameters of the model were estimated with the maximum likelihood method and updated with Bayesian inference when new data was available. Finally, the effectiveness of the proposed method was validated by the USDT data of the bottleneck system from a semiconductor assembly and test factory.

Do all shocks produce embedded herding and bubble? An empirical observation of the Indian stock market

Herding has a history of igniting large, irrational market ups and downs, usually based on a lack of fundamental support. Intuitively, most herds start with an external shock. This empirical study seeks to detect shock-induced herding and the creation of nascent bubbles in the Indian stock market. Initially, the multifractal form of the detrended fluctuation analysis was applied. Then the Reformulated Hurst exponent for the Bombay stock exchange (BSE) was determined using Kantelhardt’s calibration. The investigation found evidence of high-level herding and a bubble in 2012, with a high value of Hurst Exponent (0.7349). The other years of the research period (2011, 2013, 2016, 2018, 2020–2021) observed mild to significant herding with comparatively lower Hurst values. The results confirm that herding behavior occurs during a crisis and harsh situations emitting shocks. The study concludes that shock-based herding is prevalent in all six shocks: the economic meltdown, commodities and currency devaluation, geo-political problems, the Central Bank’s decision on liquidity management, and the Pandemic. Additionally, the years following the Financial Crisis and the years of the Pandemic are when herding and bubble are prominent. AcknowledgmentsWe thank Dr. Bikramaditya Ghosh (Associate Professor, Symbiosis International University, Bangalore, India) for motivating us in this research. We also thank Dr. Natchimuthu N (Assistant Professor, Commerce, CHRIST (Deemed to be University), Bangalore, India) and Dr. Mahesh E. (Assistant Professor, Economics, CHRIST (Deemed to be University), Bangalore, India) for their support throughout this study.

Power spectral density-based fractal analyses of sputtered yttria-stabilized zirconia thin films

This study provides information about the surface morphology of sputtered yttria-stabilized zirconia (YSZ) thin films from the atomic force microscope (AFM) spectral analyses using the power spectral density (PSD) function at varying annealing temperatures. Applying fractal and k-correlation fitting models to the PSD data, fractal dimension, Hurst exponent, correlation length, and equivalent root mean square roughness are quantified. The PSDs of the films exhibit an inverse power-law variation at high spatial frequency, which points to the existence of the fractal components in the film’s surface. The annealing temperatures up to 900 ∘C decreased fractal dimension from 2.60 to 2. The surface roughness increased from 0.10 to 13.92 nm and from 0.04 to 3.95 nm, obtained from the statistical analyses of AFM images and the k-correlation model. The films annealed from 500 ∘C to 800 ∘C showed fine grain size morphology with Hurst exponent values from 0.40 to 0.53, indicating a homogeneous spatial roughness distribution. While the film annealed at 900 ∘C exhibited large aggregate grains morphology. The growth of a sample annealed at the temperature of 900 ∘C is more likely to be ruled by the step-edge barrier-induced mound growth and inhomogeneous spatial distribution of roughness. In contrast, normal self-affine behaviour is observed at lower annealing temperatures.

Study on the Effect of Judgment Excitation Mode to Relieve Driving Fatigue Based on MF-DFA.

Driving fatigue refers to a phenomenon in which a driver’s physiological and psychological functions become unbalanced after a long period of continuous driving, and their driving skills decline objectively. The hidden dangers of driving fatigue to traffic safety should not be underestimated. In this work, we propose a judgment excitation mode (JEM), which adds secondary cognitive tasks to driving behavior through dual-channel human–computer interaction, so as to delay the occurrence of driving fatigue. We used multifractal detrended fluctuation analysis (MF-DFA) to study the dynamic properties of subjects’ EEG, and analyzed the effect of JEM on fatigue retardation by Hurst exponent value and multifractal spectrum width value. The results show that the multifractal properties of the two driving modes (normal driving mode and JEM) are significantly different. The JEM we propose can effectively delay the occurrence of driving fatigue, and has good prospects for future practical applications.

Forex market forecasting with two-layer stacked Long Short-Term Memory neural network (LSTM) and correlation analysis

Since it is one of the world's most significant financial markets, the foreign exchange (Forex) market has attracted a large number of investors. Accurately anticipating the forex trend has remained a popular but difficult issue to aid Forex traders' trading decisions. It is always a question of how precise a Forex prediction can be because of the market's tremendous complexity. The fast advancement of machine learning in recent decades has allowed artificial neural networks to be effectively adapted to several areas, including the Forex market. As a result, a slew of research articles aimed at improving the accuracy of currency forecasting has been released. The Long Short-Term Memory (LSTM) neural network, which is a special kind of artificial neural network developed exclusively for time series data analysis, is frequently used. Due to its high learning capacity, the LSTM neural network is increasingly being utilized to predict advanced Forex trading based on previous data. This model, on the other hand, can be improved by stacking it. The goal of this study is to choose a dataset using the Hurst exponent, then use a two-layer stacked Long Short-Term Memory (TLS-LSTM) neural network to forecast the trend and conduct a correlation analysis. The Hurst exponent (h) was used to determine the predictability of the Australian Dollar and United States Dollar (AUD/USD) dataset. TLS-LSTM algorithm is presented to improve the accuracy of Forex trend prediction of Australian Dollar and United States Dollar (AUD/USD). A correlation study was performed between the AUD/USD, the Euro and the Australian Dollar (EUR/AUD), and the Australian Dollar and the Japanese Yen (AUD/JPY) to see how AUD/USD movement affects EUR/AUD and AUD/JPY. The model was compared with Single-Layer Long Short-Term (SL-LSTM), Multilayer Perceptron (MLP), and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise–Improved Firefly Algorithm Long Short-Term Memory. Based on the evaluation metrics Mean Square Error (MSE), Root Mean Square Error, and Mean Absolute Error, the suggested TLS-LSTM, whose data selection is based on the Hurst exponent (h) value of 0.6026, outperforms SL-LSTM, MLP, and CEEMDAN-IFALSTM. The correlation analysis conducted shows both positive and negative relations between AUD/USD, EUR/AUD, and AUD/JPY which means that a change in AUD/USD will affect EUR/AUD and AUD/JPY as recorded depending on the magnitude of the correlation coefficient (r).