Motion Time Series Research Articles

Comparison of CNN and SVM Approaches for Classifying Time Series of Caenorhabditis Elegans Motion

Studying the motion of some roundworms types such as Caenorhabditis elegans (CE) is important to identify the actions and reactions and their effects of worm’s life. In this study, the time series of CE motion represented by the angles of wave-motion between 1 to 177 degrees will be the case study. Each observation of this time series is a recorded frame (0.5 second) of 2.5 hours video of CE motion. A convolutional neural network (CNN) as one of deep learning techniques will be used to classify CE motion as dependent variable in binary cases based on the images of the angles of wave-motion as explanatory variable. The images of motion angles are imagined and designed by two dimensions image corresponding to every observation. These images combined into 4-d image (four dimensions matrix) to represent univariate explanatory variable. Support vector machine (SVM) will be also used to classify the angles of CE. In these types of data, the nonlinearity and uncertainty will be the most probably problems as reasons for in accurate classifications. CNN and SVM used with this type of dataset to improve the classification results. The results of comparisons explain that CNN approach outperforms SVM absolutely. In conclusion, CNN approach can be used to classify this type of time series with accurate results.

Predicting and analyzing the three-dimensional spatiotemporal evolution process of tidal currents by using a brand new machine learning algorithm

A machine learning algorithm was developed for efficiently predicting the 3D (three-dimensional) spatiotemporal evolution process of tidal currents and analyzing their spatial distribution characteristics. In the algorithm, an extremely simplified multi-layer perceptron architecture, an embedded spatial information learning method, and a splicing-sharing method for tidal currents at different water depths were used to achieve a high-coverage, comprehensive, and systematic 3D tidal current prediction of the study area. The developed algorithm can efficiently predict the future time series of three-dimensional tidal current movement and solves the problem that existing algorithms are unable to analyze the similarity of the three-dimensional spatiotemporal distribution of tidal currents over many years. In this study, 3D tidal current evolutions in the southern waters of Liaoning Province, China, were analyzed. The Finite-Volume Coastal Ocean Model ocean model was used to simulate tidal currents in the study zone, generating a dataset to train the developed machine learning model. The trained model was then used to predict and analyze tidal currents. The prediction results show that the developed machine learning model has high prediction accuracy for tidal currents over a future period of 12 h, with R2 (R-Square) of 0.871, mean absolute error of 0.047 m/s and root mean square error of 0.152 m/s. Additionally, the developed machine learning model could effectively analyze the correlation of spatial distribution characteristics of tidal currents at different water depths, and tidal currents with similar evolution processes at different zones could also be classified.

Investigation into the Prediction of Ship Heave Motion in Complex Sea Conditions Utilizing Hybrid Neural Networks

While navigating at sea, ships are influenced by various factors, including wind, waves, and currents, which can result in heave motion that significantly impacts operations and potentially leads to accidents. Accurate forecasting of ship heaving is essential to guarantee the safety of maritime navigation. Consequently, this paper proposes a hybrid neural network method that combines Convolutional Neural Networks (CNNs), Bidirectional Long Short-Term Memory Networks (BiLSTMs), and an Attention Mechanism to predict the heaving motion of ships in moderate to complex sea conditions. The data feature extraction ability of CNNs, the temporal analysis capabilities of BiLSTMs, and the dynamic adjustment function of Attention on feature weights were comprehensively utilized to predict a ship’s heave motion. Simulations of a standard container ship’s motion time series under complex sea state conditions were carried out. The model training and validation results indicate that, under sea conditions 4, 5, and 6, the CNN-BiLSTM-Attention method demonstrated significant improvements in MAPE, APE, and RMSE when compared to the traditional LSTM, Attention, and LSTM-Attention methods. The CNN-BiLSTM-Attention method could enhance the accuracy of the prediction. Heave displacement, pitch displacement, pitch velocity, pitch acceleration, and incoming wave height were chosen as key input features. Sensitivity analysis was conducted to optimize the prediction performance of the CNN-BiLSTM-Attention hybrid neural network method, resulting in a significant improvement in MAPE and enhancing the accuracy of ship motion prediction. The research presented in this paper establishes a foundation for future studies on ship motion prediction.

Object oriented data analysis of surface motion time series in peatland landscapes

Abstract Peatlands account for 10% of UK land area, 80% of which are degraded to some degree, emitting carbon at a similar magnitude to oil refineries or landfill sites. A lack of tools for rapid and reliable assessment of peatland condition has limited monitoring of vast areas of peatland and prevented targeting areas urgently needing action to halt further degradation. Measured using interferometric synthetic aperture radar (InSAR), peatland surface motion is highly indicative of peatland condition, largely driven by the eco-hydrological change in the peatland causing swelling and shrinking of the peat substrate. The computational intensity of recent methods using InSAR time series to capture the annual functional structure of peatland surface motion becomes increasingly challenging as the sample size increases. Instead, we utilize the behaviour of the entire peatland surface motion time series using object oriented data analysis to assess peatland condition. Bayesian cluster analysis based on the functional structure of the surface motion time series finds areas indicative of soft/wet peatlands, drier/shrubby peatlands, and thin/modified peatlands. The posterior distribution of the assigned peatland types enables the scale of peatland degradation to be assessed, which will guide future cost-effective decisions for peatland restoration.

Machine-learning-based virtual load sensors for mooring lines using simulated motion and lidar measurements

Abstract. Floating offshore wind turbines (FOWTs) are equipped with various sensors that provide valuable data for turbine monitoring and control. Due to technical and operational challenges, load estimations for mooring lines and fairleads can be difficult and expensive to obtain accurately. This research delves into a methodology where simulated floater motion measurements and wind speed measurements, derived from forward-looking nacelle-based lidar, are utilized as inputs for different types of neural networks to estimate fairlead tension time series and damage equivalent loads (DELs). Fairlead tension is intrinsically linked to the dynamics and the position of the floater. Therefore, we systematically analyze the individual contribution of floater dynamics to the prediction quality of fairlead tension time series and DELs. Wind speed measurements obtained via nacelle-based lidar on floating offshore wind turbines are inherently influenced by the platform's dynamics, notably the rotational pitch displacement and surge displacement of the floater. Consequently, the lidar wind speed data indirectly contain the dynamic behavior of the floater, which, in turn, governs the fairlead loads. This study leverages lidar-measured line-of-sight (LOS) wind speeds to estimate fairlead tensions. Training data for the model are generated by the aeroelastic wind turbine simulation tool, openFAST, in conjunction with the numerical lidar simulation framework ViConDAR. The fairlead tension time series are predicted using long short-term memory (LSTM) networks. DEL predictions are made using three different approaches. First, DELs are calculated from predicted time series; second, DELs are predicted using a sequence-to-one LSTM architecture, and third, DELs are predicted using a convolutional neural network architecture. Results indicate that fairlead tension time series and DELs can be accurately estimated from floater motion time series. Further, we found that lidar LOS measurements do not improve time series or DEL predictions if motion measurements are available. However, using lidar measurements as model inputs for DEL predictions leads to similar accuracies as using displacement measurements of the floater.

Wearable Activity Recognition for Advancing Elderly Care with Modified Transformer Model

Technological devices such as smartphones can be utilized in tracking various human activities or movements through built-in accelerometers and gyroscopes. Data obtained from these inertial sensors can be utilized in various applications to assist people, including healthcare, human-computer interaction, and sports. As a result, further developments in the effective classification of time series data through machine and deep learning is highly valued and actively pursued. In this study, the transformer model, a deep learning architecture designed for sequential data such as natural language processing (NLP), has been utilized for analysis of time-series motion readings from wearable accelerometers. The transformer model in this study has been refined by incorporating a Long Short-Term Memory (LSTM) recurrent neural network (RNN) architecture. By leveraging the HAR70+ dataset with a wide range of activities, the modified transformer model in this study obtained a best accuracy of 95.85%, demonstrating that it can match the performance of state-of-the-art wearable activity recognition methods using Deep Neural Networks (DNN) and LSTM. Hence, the findings presented in this study suggest the future relevance of improved transformer or deep learning models to enhance the quality of life for seniors.

Motion process and failure mode of Pusa landslide, China based on dense optical flow method

ABSTRACT Unmanned aerial vehicle (UAV) is widely applied in geohazard monitoring with its high resolution and feasibility features, where UAV videos can record the whole landslide failure process. Previous studies can only provide the qualitative depiction of the landslide failure process, rather than the quantitative motion process, which makes it difficult to analyse the landslide dynamic characteristics and failure mode. In this letter, we take UAV video of Pusa landslide, China obtained on 28 August 2017 to retrieve the landslide motion process by using the dense optical flow method. Firstly, the landslide boundary can be clearly depicted by the cumulative landslide motion time series maps. Secondly, the maximum cumulative motion distance of the Pusa landslide was located in the middle of the slope body, with the maximum distance as 79 m, while the maximum instantaneous motion rate was around 42 m/s in the middle and lower part of the slope body. Finally, the failure mode of Pusa landslide can be characterized as ‘fissure zone in the middle, fissure extension to the top, rock bulges outward in the middle and landslide failure to high-speed runout debris flow’.

Detecting Instantaneous Tidal Signals in Ocean Models Utilizing Streaming Band‐Pass Filters

AbstractThrough the implementation of a streaming filter, output of numerical ocean simulations can be band‐pass filtered at tidal frequencies while the model is running, yielding time series of sinusoidal motions consisting of tidal signals in the filter's target frequency band. The filtering algorithm is developed from a system of two ordinary differential equations that represents the motion of a damped harmonic oscillator. The filter's response to a broadband input signal is unity at its target frequency but vanishes toward the low and high frequency limits. The decay of the filter response is controlled by a dimensionless parameter, which determines the filter's bandwidth. As a result, the filter allows signals within a small frequency band around its target frequency to pass through, while blocking signals outside of its target frequency band. In this work, the filtering algorithm is implemented into the barotropic solver of the Modular Ocean Model version 6 (MOM6) for determining the instantaneous tidal velocities of the semi‐diurnal and diurnal tides. Utilizing the filters, the frequency‐dependent internal wave drag is applied to the semi‐diurnal and diurnal frequency bands separately. The simulation results suggest that the performance of the algorithm is consistent with the filter transfer function in Fourier space. Potential applications of the algorithm also include de‐tiding the model output for nested regional ocean models, especially those for the purpose of operational forecasting.

Interpreting the Projected Frontal Area in Front Crawl: Determining the Projected Frontal Area of Each Body Segment.

This study aimed to provide evidence for the interpretation of the projected frontal area (PFA) during front crawl. To achieve this goal, we developed a method for calculating the PFA of each body segment using digital human technology and compared the pressure drag under two calculation conditions: a combination of the PFA with and without accounting for the horizontal velocity of each body segment. Twelve competitive male swimmers performed a 15-meter front crawl at 1.20 m·s-1. The three-dimensional positions of the reflective markers attached to the swimmer's body were recorded using an underwater motion-capture system. Based on the body shape of each swimmer obtained from the photogenic body scanner, individual digital human body models were created with the color of the model's vertices divided into eight body segments. The time series of the volumetric swimming motion was reconstructed using inverse kinematics. The PFA of each body segment was then calculated by the automatic processing of a series of parallel frontal images. The pressure drag index, defined as the value excluding the drag coefficient while simultaneously considering the PFA and the horizontal velocity, was calculated under two conditions: the static condition (accounting for only the PFA of each body segment) and the dynamic condition (accounting for the PFA and horizontal velocity of each body segment). Notably, the pressure drag index was higher under the static condition than under the dynamic condition for the humerus, ulna, and hand segments (p < 0.001). The results obtained using our methodology indicate that the PFA of the upper limb segments overestimates their contribution to pressure drag during front crawl under the static condition.

Advancing polar motion prediction with derivative information

Abstract Earth Orientation Parameters (EOP) are essential for monitoring Earth’s rotational irregularities, impacting satellite navigation, space exploration, and climate forecasting. This study introduces a hybrid prediction model combining least-squares (LS) and vector autoregression (VAR) to improve Earth’s Pole Coordinates (x, y) forecast accuracy. Using daily sampled IERS EOP 20 C04 data from 2013 to 2023, we conducted 1,000 yearly random trials, performing 48 forecasts per year. Our method evaluates six data combinations, including primary variables (x, y) and their derivatives ( x ̇ , y ̇ $\dot{x},\dot{y}$ ). Results show a systematic improvement in prediction accuracy, especially for ultra-short-term forecasts (10 days into future), with derivative information stabilizing the solutions. The best-performing combination ( x , y , x ̇ , y ̇ $x,y,\dot{x},\dot{y}$ ) achieved a mean absolute prediction error (MAPE) reduction (with respect to the reference data combination – x, y) of up to 8 % for the y and 7 % for the x over a whole 30-day forecast horizon. These findings highlight the effectiveness of incorporating derivatives of polar motion time series into prediction procedure.

Detection of slow slip events along the southern Peru - northern Chile subduction zone

Detections of slow slip events (SSEs) are now common along most plate boundary fault systems at the global scale. However, no such event has been described in the south Peru - north Chile subduction zone so far, except for the early preparatory phase of the 2014 Iquique earthquake. We use geodetic template matching on GNSS-derived time series of surface motion in Northern Chile to extract SSEs hidden within the geodetic noise. We detect 33 events with durations ranging from 9 to 40 days and magnitudes from Mw 5.6 to 6.2. The moment released by these aseismic events seems to scale with the cube of their duration, suggesting a dynamic comparable to that of earthquakes. We compare the distribution of SSEs with the distribution of coupling along the megathrust derived using Bayesian inference on GNSS- and InSAR-derived interseismic velocities. From this comparison, we obtain that most SSEs occur in regions of intermediate coupling where the megathrust transitions from locked to creeping or where geometrical complexities of the interplate region have been proposed. We finally discuss the potential role of fluids as a triggering mechanism for SSEs in the area.

Interpersonal Motor Coordination in Children with Autism and the Establishment of Machine Learning Models to Objectively Classify Children with Autism and Typical Development

BackgroundThe global prevalence of autism spectrum disorder (ASD) is around 1%. Yet the current diagnosis of ASD mainly depends on clinicians' experience and caregivers' report, which are subjective, time consuming, and labor demanding. An objective and efficient way to diagnose ASD is urgently needed. The objective of this study was to quantify an omnipresent yet least studied behavioral characteristic in children with ASD – interpersonal motor coordination (IMC), and to investigate the feasibility of using IMC related features to identify ASD by implementing machine learning algorithms. MethodsTwenty children with ASD and twenty-three children with typical development (TD) were filmed in a conversation with an interviewer. Motion energy analysis was implemented to obtain the movement time series, and cross wavelet analysis (CWA) quantified the level of IMC at different movement frequencies. Machine learning algorithms were utilized to examine whether these two groups of children could be accurately classified using features of IMC. ResultsStatistical analysis revealed reduced IMC in the ASD group at relatively high movement frequencies. The establishment of machine learning (ML) models showed that the maximum classification accuracy was 85.37% (specificity = 95.24%, sensitivity = 75.00%) using five original coherence values computed with CWA. In addition, the classification accuracy could be improved to 92.68% (specificity = 95.24%, sensitivity = 90.00%) with three novel features created by taking the sum of statistically significant features. ConclusionsChildren with ASD demonstrated an atypical profile of IMC, and IMC could be used to objectively classify children with ASD and TD. In addition, our analyses showed that creating novel features based on statistically significant features could help improve classification performance. It is proposed that such economic, contactless, and calibration-free approach to data collection might well serve both ASD research and practice, particularly early objective identification. However, this study could be improved with respect to larger sample size with balanced gender ratio and different severity.

Validation of OpenCap: A low-cost markerless motion capture system for lower-extremity kinematics during return-to-sport tasks

Low-cost markerless motion capture systems offer the potential for 3D measurement of joint angles during human movement. This study aimed to validate a smartphone-based markerless motion capture system’s (OpenCap) derived lower extremity kinematics during common return-to-sport tasks, comparing it to an established optoelectronic motion capture system. Athletes with prior anterior cruciate ligament reconstruction (12–18 months post-surgery) performed three movements: a jump-landing-rebound, single-leg hop, and lateral-vertical hop. Kinematics were recorded concurrently with two smartphones running OpenCap’s software and with a 10-camera, marker-based motion capture system. Validity of lower extremity joint kinematics was assessed across 437 recorded trials using measures of agreement (coefficient of multiple correlation: CMC) and error (mean absolute error: MAE, root mean squared error: RMSE) across the time series of movement. Agreement was best in the sagittal plane for the knee and hip in all movements (CMC > 0.94), followed by the ankle (CMC = 0.84–0.93). Lower agreement was observed for frontal (CMC = 0.47–0.78) and transverse (CMC = 0.51–0.6) plane motion. OpenCap presented a grand mean error of 3.85° (MAE) and 4.34° (RMSE) across all joint angles and movements. These results were comparable to other available markerless systems. Most notably, OpenCap’s user-friendly interface, free software, and small physical footprint have the potential to extend motion analysis applications beyond conventional biomechanics labs, thus enhancing the accessibility for a diverse range of users.

Head Gesture Recognition Combining Activity Detection and Dynamic Time Warping.

The recognition of head movements plays an important role in human-computer interface domains. The data collected with image sensors or inertial measurement unit (IMU) sensors are often used for identifying these types of actions. Compared with image processing methods, a recognition system using an IMU sensor has obvious advantages in terms of complexity, processing speed, and cost. In this paper, an IMU sensor is used to collect head movement data on the legs of glasses, and a new approach for recognizing head movements is proposed by combining activity detection and dynamic time warping (DTW). The activity detection of the time series of head movements is essentially based on the different characteristics exhibited by actions and noises. The DTW method estimates the warp path distances between the time series of the actions and the templates by warping under the time axis. Then, the types of head movements are determined by the minimum of these distances. The results show that a 100% accuracy was achieved in the task of classifying six types of head movements. This method provides a new option for head gesture recognition in current human-computer interfaces.

Leveraging an intensive time series of young children's movement to capture impulsive and inattentive behaviors in a preschool setting.

Studying within-person variability in children's behavior is frequently hindered by challenges collecting repeated observations. This study used wearable accelerometers to collect an intensive time series (2.7 million observations) of young children's movement at school (N = 62, Mage = 4.5 years, 54% male, 74% Non-Hispanic White) in 2021. Machine learning analyses indicated that children's typical forward acceleration was strongly correlated with lower teacher-reported inhibitory control and attention (r = -.69). Using forward movement intensity as a proxy for impulsivity, we partitioned the intensive time series and found that (1) children modulated their behavior across periods of the school day, (2) children's impulsivity increased across the school week, and (3) children with greater impulsivity showed greater variability in behavior across days.

Forecasting surface movements based on PSI time series using machine learning algorithms

ABSTRACT Surface movements pose a critical issue requiring prompt detection and monitoring to ensure safety. To address this concern, the detection and continuous monitoring of surface deformations have gained importance. While numerous point-based surveying methods exist, multi-temporal interferometric synthetic aperture radar (InSAR) analysis has emerged as a powerful technique capable of detecting deformations across large areas with freely available SAR images and software. However, the significance of surface movement forecasting must be addressed, as it plays a significant role in preventing accidents and implementing precautionary measures. In light of this, a comprehensive study was conducted at the new Istanbul Airport in Türkiye, employing the Persistent Scatterer InSAR (PSI) method with a collection of 211 Sentinel-1 SAR images. The results obtained were investigated, and six test case regions were determined for the forecasting analysis in terms of time series movement type (subsidence, uplift, and stable) and structure type (runway and building) using various machine learning (ML) algorithms. To accomplish this, regression-based and sequential-based ML algorithms were employed and compared, showing the potential of cutting-edge techniques. The Stacked LSTM algorithm was the most effective in generating accurate forecasts. Furthermore, by incorporating exogenous variables into the forecasting analysis, the study improved the accuracy of the results. To gain deeper insights into the impact of these exogenous variables, feature importance analysis was conducted using the permutation feature importance method. The results obtained were examined, considering both the structure type and the characteristics of the time series data.

Full seismic waveform analysis combined with transformer neural networks improves coseismic landslide prediction

Seismic waves can shake mountainous landscapes, triggering thousands of landslides. Regional-scale landslide models primarily rely on shaking intensity parameters obtained by simplifying ground motion time-series into peak scalar values. Such an approach neglects the contribution of ground motion phase and amplitude and their variations over space and time. Here, we address this problem by developing an explainable deep-learning model able to treat the entire wavefield and benchmark it against a model equipped with scalar intensity parameters. The experiments run on the area affected by the 2015 Mw7.8 Gorkha, Nepal earthquake reveal a 16% improvement in predictive capacity when incorporating full waveforms. This improvement is achieved mainly on gentle (~25°) hillslopes exposed to low ground shaking (~0.2 m/s). Moreover, we can largely attribute this improvement to the ground motion before and much after the peak velocity arrival. This underscores the limits of single-intensity measures and the untapped potential of full waveform information.

Ground-motion simulations using two-dimensional convolution condition adversarial neural network(2D-cGAN)

In this paper, an integrated framework based on conditional adversarial neural network (cGAN) is established to simulate ground motions for earthquake scenarios with different magnitude, distance, and local site conditions. A ground motion dataset is created for training the network, within which most data are observed accelerograms collected from PEER and gaps for certain magnitude-site conditions are filled with accelerograms simulated using stochastic finite-fault modeling. During the learning of cGAN, the dataset is classified first with multi-labels according to local site conditions, and the multi-labels are set to be the conditional information Y for the network. Effects of using one-dimensional convolution (Conv1D) and two-dimensional convolution (Conv2D) in cGAN are tested in terms of the time-domain and frequency-domain characteristics of the generated ground motion. The test proves the strengths of Conv2D in capturing high-dimensional temporal and spectral characteristics from one-dimensional time series of ground motion. Ground motions generated using 2D-cGAN network are compared to the measures predicted by widely-used ground motion prediction equations, through which the reliability of 2D-cGAN network on ground motion simulation is verified.

Оцінка стабільності дамби водосховища за допомогою методу постійних розсіювачів INSAR С-діапазону

The purpose of this article is to analyze the results of processing time series of radar images using the Persistent Scatterer method to assess the stability of the vertical position of the reservoir dam. The object of this study is the dam of the cooling pond at the Khmelnytskyi Nuclear Power Plant. Due to production needs, the task arose to analyze the dam's stability in the vertical position using an independent method for the 2016-2022 period. Implementing such a task became possible only by utilizing a satellite radar image database for the specified area. The input data for the analysis consisted of 13 radar images of the specified area obtained from the Sentinel-1 satellite, covering the period from May 2016 to May 2022 with a six-month interval. Processing satellite radar data using the StaMPS algorithm allowed for creation of maps of average surface movement velocities. After applying spatial-correlated and tropospheric corrections, the vertical velocity range of the developed deformation maps for the investigated area was [-9.0; +8.3] mm/year. At the industrial site area, the average velocities of vertical displacements are close to zero, this indicates the stability of the specified area according to InSAR observations. Analyzing the plots of vertical movements of the dam it was observed that the displacements exhibit a cyclic pattern, which is associated with seasonal influences on the structure. The magnitude of maximum displacements during the investigated period ranged from [-10 mm; +10 mm]. The obtained data indicate the absence of hazardous deformation processes that could affect the operational reliability of the reservoir dam. A comparative analysis of the results with time series of vertical movements of reservoir dams in Poland (Niedzica Dam, Solina Dam, Włocławek Dam) was performed. The time series obtained from the European Ground Motion Service data confirm the presence of seasonal cyclic movements of the dams. The practical significance of the research results lies in confirming the effectiveness of using a time series of C-band radar images for geodetic monitoring of reservoir dam stability. Due to access to the existing database of radar images of the Sentinel-1 satellite, the task of assessing the stability of the vertical position of the dam of the cooling reservoir of the Khmelnytsky NPP for the period from 2016 to 2022 was solved.

A Hybrid GARCH and Deep Learning Method for Volatility Prediction

Volatility prediction plays a vital role in financial data. The time series movements of stock prices are commonly characterized as highly nonlinear and volatile. This study is aimed at enhancing the accuracy of return volatility forecasts for stock prices by investigating the prediction of their price volatility through the integration of diverse models. Thus, the study integrated four powerful methods: seasonal autoregressive (AR) integrated moving average (MA), generalized AR conditional heteroskedasticity (ARCH) family models, convolutional neural network (CNN), and bidirectional long short‐term memory (LSTM) network. The hybrid model was developed using the residuals generated by the seasonal AR integrated MA model as input for the generalized ARCH model. Following this, the estimated volatility obtained was utilized as an input feature for both the hybrid CNNs and bidirectional LSTM models. The model’s forecasting performance was assessed using key evaluation metrics, including mean absolute error (MAE) and root mean squared error (RMSE). Compared to other hybrid models, our new proposed hybrid model demonstrates an average reduction in MAE and RMSE of 60.35% and 60.61%, respectively. The experimental results show that the model proposed in this study has good performance and accuracy in predicting the volatility of stock prices. These findings offer valuable insights for financial data analysis and risk management strategies.