Correlated Time Series Research Articles

Universality of Dynamical Symmetries in Chaotic Maps

Identifying signs of regularity and uncovering dynamical symmetries in complex and chaotic systems is crucial both for practical applications and for enhancing our understanding of complex dynamics. Recent approaches have quantified temporal correlations in time series, revealing hidden, approximate dynamical symmetries that provide insight into the systems under study. In this paper, we explore universality patterns in the dynamics of chaotic maps using combinations of complexity quantifiers. We also apply a recently introduced technique that projects dynamical symmetries into a “symmetry space”, providing an intuitive and visual depiction of these symmetries. Our approach unifies and extends previous results and, more importantly, offers a meaningful interpretation of universality by linking it with dynamical symmetries and their transitions.

MSDG: Multi-Scale Dynamic Graph Neural Network for Industrial Time Series Anomaly Detection

A large number of sensors are typically installed in industrial plants to collect real-time operational data. These sensors monitor data with time series correlation and spatial correlation over time. In previous studies, GNN has built many successful models to deal with time series data, but most of these models have fixed perspectives and struggle to capture the dynamic correlations in time and space simultaneously. Therefore, this paper constructs a multi-scale dynamic graph neural network (MSDG) for anomaly detection in industrial sensor data. First, a multi-scale sliding window mechanism is proposed to input different scale sensor data into the corresponding network. Then, a dynamic graph neural network is constructed to capture the spatial–temporal dependencies of multivariate sensor data. Finally, the model comprehensively considers the extracted features for sequence reconstruction and utilizes the reconstruction errors for anomaly detection. Experiments have been conducted on three real public datasets, and the results show that the proposed method outperforms the mainstream methods.

Mean square consistency and improved rate of convergence of generalized subsampling estimator for non‐stationary time series

In this article, we show the mean square consistency for a generalized subsampling estimator based on the aggregation of the mean, median, and trimmed mean of some subsampling estimators for general non‐stationary time series. Consistency requires standard assumptions, including the existence of moments and ‐mixing conditions. We apply our results to the Fourier coefficients of the autocovariance function of periodically correlated time series. Furthermore, as in the i.i.d. case, we show that the generalized subsampling estimator satisfies Bernstein inequality and concentrates at an improved rate (under the condition of no or small bias) compared with the original estimator. Finally, we illustrate our results with some simulation data examples.

Time series trends and correlations of aerosol optical depth and cloud parameters over Addis Ababa

Aerosols are microscopic liquid or solid particles that enter the atmosphere through natural and man-made processes. Time series trends and correlations of aerosol optical depth and cloud parameters over Addis Ababa have become the subject of scientific research because of the importance of clouds in controlling climate. In this study, we have examined the temporal variations (time series analysis) in aerosol particles over Addis Ababa and the impact of these variations on various optical properties of clouds using Moderate Resolution Imaging Spectroradiometer (MODIS) data from January 2003 to December 2018. The maximum aerosol optical depth (AOD) was found during the summer period, with minimum values in winter. During summer, the air temperature is high, which leads to abundant atmospheric water vapor, facilitating the hygroscopic growth of aerosols. We then analyzed the relationships between AOD and other cloud parameters, namely, water vapor (WV), cloud fraction (CF), cloud top temperature (CTT), and cloud top pressure (CTP), to provide a better understanding of aerosol–cloud interactions. The correlation between AOD and CF and WV was positive for Addis Ababa, while there was a negative correlation with CTT and CTP.

Detection of Movement and Lead-Popping Artifacts in Polysomnography EEG Data

Polysomnography (PSG) measures brain activity during sleep via electroencephalography (EEG) using six leads. Artifacts caused by movement or loose leads distort EEG measurements. We developed a method to automatically identify such artifacts in a PSG EEG trace. After preprocessing, we extracted power levels at frequencies of 0.5–32.5 Hz with multitaper spectral analysis using 4 s windows with 3 s overlap. For each resulting 1 s segment, we computed segment-specific correlations between power levels for all pairs of leads. We then averaged all pairwise correlation coefficients involving each lead, creating a time series of segment-specific average correlations for each lead. Our algorithm scans each averaged time series separately for “bad” segments using a local moving window. In a second pass, any segment whose averaged correlation is less than a global threshold among all remaining good segments is declared an outlier. We mark all segments between two outlier segments fewer than 300 s apart as artifact regions. This process is repeated, removing a channel with excessive outliers in each iteration. We compared artifact regions discovered by our algorithm to expert-assessed ground truth, achieving sensitivity and specificity of 80% and 91%, respectively. Our algorithm is an open-source tool, either as a Python package or a Docker.

Spatial–Temporal-Correlation-Constrained Dynamic Graph Convolutional Network for Traffic Flow Forecasting

Accurate traffic flow prediction in road networks is essential for intelligent transportation systems (ITS). Since traffic data are collected from the road network with spatial topological and time series sequences, the traffic flow prediction is regarded as a spatial–temporal prediction task. With the powerful ability to model the non-Euclidean data, the graph convolutional network (GCN)-based models have become the mainstream framework for traffic forecasting. However, existing GCN-based models either use the manually predefined graph structure to capture the spatial features, ignoring the heterogeneity of road networks, or simply perform 1-D convolution with fixed kernel to capture the temporal dependencies of traffic data, resulting in insufficient long-term temporal feature extraction. To solve those issues, a spatial–temporal correlation constrained dynamic graph convolutional network (STC-DGCN) is proposed for traffic flow forecasting. In STC-DGCN, a spatial–temporal embedding encoder module (STEM) is first constructed to encode the dynamic spatial relationships for road networks at different time steps. Then, a temporal feature encoder module with heterogeneous time series correlation modeling (TFE-HCM) and a spatial feature encoder module with dynamic multi-graph modeling (SFE-DCM) are designed to generate dynamic graph structures for effectively capturing the dynamic spatial and temporal correlations. Finally, a spatial–temporal feature fusion module based on a gating fusion mechanism (STM-GM) is proposed to effectively learn and leverage the inherent spatial–temporal relationships for traffic flow forecasting. Experimental results from three real-world traffic flow datasets demonstrate the superior performance of the proposed STC-DGCN compared with state-of-the-art traffic flow forecasting models.

Disentangled traffic forecasting via efficient graph neural network

Abstract Traffic prediction is important to intelligent transportation systems, but it poses significant challenges due to the complex spatio-temporal correlation of traffic data. To address these challenges, we decompose complex traffic time series into events and trends using discrete wavelet transform. However, the high-frequency information decomposed by wavelet transform contains noise, so we designed a module to denoise the high-frequency events. We model the spatio-temporal correlations of trends and events separately using two mutually independent spatio-temporal networks. We use causal dilation convolution with local receptive fields and attention with global receptive fields to capture the correlation of fluctuating time series and the correlation of stable time series, respectively. We capture spatial correlation using a GNN optimized by an attention mechanism. Finally, we merge useful information from volatile events into predictable trends using adaptive event fusion. Our model significantly outperforms nine existing traffic prediction methods across four real datasets.

A novel and effective method for characterizing time series correlations based on martingale difference correlation.

Analysis of correlation between time series is an essential step for complex system studies and dynamical characteristics extractions. Martingale difference correlation (MDC) theory is mainly concerned with the correlation of conditional mean values between response variables and predictor variables. It is the generalization and deepening of the Pearson correlation coefficient, Spearman correlation coefficient, Kendall correlation coefficient, and other statistics. In this paper, on the basis of phase space reconstruction, the generalized dependence index (GDI) is proposed by using MDC and martingale difference divergence matrix theories, which can measure the degree of dependence between time series more effectively. Moreover, motivated by the theoretical framework of the refined distance correlation method, the corresponding dependence measure (DE) is employed in this paper to construct the DE-GDI plane, so as to comprehensively and intuitively distinguish different types of data and deeply explore the operating mechanism behind the relevant time series and complex systems. According to the performances tested by the different simulated and real-world data, our proposed method performs relatively reasonably and reliably in dependence measuring and data distinguishing. The proposal of this complex data clustering method can not only recognize the features of complex systems but also distinguish them effectively so as to acquire more relevant detailed information.

THE ROLE OF THE GREEN ECONOMY IN SHAPING ECONOMIC GROWTH IN POLAND

The aim of this paper is to examine and understand the impact of various green economy indicators on economic growth in Poland from 2010 to 2021. The study focused on a select number of indicators, including the final energy intensity of the economy, expenditures on environmental fixed assets in relation to gross domestic product (GDP), the share of renewable electricity in gross final electricity consumption, primary energy intensity of GDP, and the percentage of urban green areas. The relationship between green economy indicators and economic growth, expressed as gross domestic product per capita, was examined using regression analysis, time series analysis and correlation analysis. Data for the analysis were taken from the Central Statistical Office. Time trend analysis showed that the economy’s final energy intensity and the share of renewable energy improved steadily over the period under review, with a positive impact on GDP per capita. Correlation analysis demonstrated a robust inverse correlation between energy intensity and GDP per capita, along with a positive association between the share of renewable energy and economic growth. In linear and multiple regressions, the economy’s final energy intensity, expenditures on environmental fixed assets, and the share of renewable energy exhibited a significant impact on GDP per capita. The study’s conclusions underscore the necessity of sustained and intensified efforts towards a green economy in Poland, which is pivotal for ensuring long-term economic growth and sustainable development.

Periodically correlated time series and the Variable Bandpass Periodic Block Bootstrap.

This research introduces a novel approach to resampling periodically correlated time series using bandpass filters for frequency separation called the Variable Bandpass Periodic Block Bootstrap and then examines the significant advantages of this new method. While bootstrapping allows estimation of a statistic's sampling distribution by resampling the original data with replacement, and block bootstrapping is a model-free resampling strategy for correlated time series data, both fail to preserve correlations in periodically correlated time series. Existing extensions of the block bootstrap help preserve the correlation structures of periodically correlated processes but suffer from flaws and inefficiencies. Analyses of time series data containing cyclic, seasonal, or periodically correlated principal components often seen in annual, daily, or other cyclostationary processes benefit from separating these components. The Variable Bandpass Periodic Block Bootstrap uses bandpass filters to separate a periodically correlated component from interference such as noise at other uncorrelated frequencies. A simulation study is presented, demonstrating near universal improvements obtained from the Variable Bandpass Periodic Block Bootstrap when compared with prior block bootstrapping methods for periodically correlated time series.

Decentralized optimal voltage control for wind farm with deep learning-based data-driven modeling

The random fluctuations of wind energy and external grid voltage disturbances can both lead to serious voltage fluctuations and voltage deviations in the wind farm (WF). Voltage/reactive power control is an effective way to improve the voltage stability of WF. The existing research is based on complex physical models with prior parameter information, and the accuracy and calculation speed of the WF model are difficult to guarantee. To address this issue, this paper explores a decentralized optimal voltage control method for WF with deep learning-based (DL) data-driven modeling (DL-DOVC). A hybrid convolutional neural network (CNN)-Transformer architecture is proposed to establish the data-driven model of WF, leveraging its enhanced capabilities for extracting time series correlation, to learn complex patterns and dynamics from time series data. Then, we develop a fully decentralized voltage control method for WF to regulate the terminal bus voltage of wind turbines (WTs) within a feasible range. A DL-based data-driven predictive controller is specially designed to solve the established data-driven voltage optimization problem, it eliminates the necessity for frequent manual model maintenance and is suitable for real-time application. Additionally, the difficulty of WF decentralized optimal voltage control arises from the inability of local controllers to fully consider the impact of all non-local WTs on the local WT states. By designing the DL-based auxiliary state-feedback controller, the effects of non-local WTs are implicitly considered in the auxiliary feedback control law. A WF with 32*6.25 MW WTs is used to test the proposed DL-DOVC method. Simulation results show that the proposed DL-based model can efficiently learn and predict the WF dynamics under different operating scenarios. The near-global optimal voltage control performance is achieved only with local measurements by employing the DL-DOVC method.

Temporal scaling theory for bursty time series with clusters of arbitrarily many events.

Long-term temporal correlations in time series in a form of an event sequence have been characterized using an autocorrelation function that often shows a power-law decaying behavior. Such scaling behavior has been mainly accounted for by the heavy-tailed distribution of interevent times, i.e., the time interval between two consecutive events. Yet, little is known about how correlations between consecutive interevent times systematically affect the decaying behavior of the autocorrelation function. Empirical distributions of the burst size, which is the number of events in a cluster of events occurring in a short time window, often show heavy tails, implying that arbitrarily many consecutive interevent times may be correlated with each other. In the present study, we propose a model for generating a time series with arbitrary functional forms of interevent time and burst size distributions. Then, we analytically derive the autocorrelation function for the model time series. In particular, by assuming that the interevent time and burst size are power-law distributed, we derive scaling relations between power-law exponents of the autocorrelation function decay, interevent time distribution, and burst size distribution. These analytical results are confirmed by numerical simulations. Our approach helps to rigorously and analytically understand the effects of correlations between arbitrarily many consecutive interevent times on the decaying behavior of the autocorrelation function.

Impact of Model Resolution and Initial/Boundary Conditions in Forecasting Low-Level Atmospheric Fields over the Incheon International Airport

Abstract This study investigates the impact of initial conditions/boundary conditions (ICs/BCs) and horizontal resolutions on forecast for average weather conditions, focusing on low-level weather variables such as 2-m temperature (T2m), 2-m water vapor mixing ratio (Q2m), and 10-m wind speed (WS10). A Weather Research and Forecasting (WRF) Model is used for regional mesoscale model simulations and large-eddy simulations (LESs). The 6-h-interval forecast fields generated by the Global Forecast System of the National Centers for Environmental Prediction and the Korean Integrated Model of the Korea Meteorological Administration are utilized as ICs/BCs for the regional models. Numerical experiments are performed for 24 h starting at 0000 UTC on each day in April 2021 when the average monthly wind speed was strongest during 10 years (2011–20). A comparison of model simulations with observations obtained around the Yeongjong Island, where Incheon International Airport is situated, shows that the regional models capture the time series of T2m, Q2m, and WS10 more effectively than the global model forecasts. Moreover, the LES experiments with a 100-m horizontal grid spacing simulate higher Q2m and lower WS10 during the daytime compared to the 1-km WRF. This results in a deterioration of their time-series correlation with the observations. Meanwhile, the 100-m LES forecasts time series of T2m over ocean stations and Q2m over land stations, as well as probability density functions of low-level weather variables, more accurately than that of the 1-km WRF. Our study also emphasizes the need for caution when comparing high-resolution model results with observation values at specific stations due to the high spatial variability in low-level meteorological fields.

Optimal choice of bootstrap block length for periodically correlated time series

Optimal choice of bootstrap block length for periodically correlated time series

AutoCTS++: zero-shot joint neural architecture and hyperparameter search for correlated time series forecasting

AutoCTS++: zero-shot joint neural architecture and hyperparameter search for correlated time series forecasting

Fast Bayesian filtering for wastewater treatment plants with inaccurate process noise statistics

Accurate state estimation of wastewater treatment plants is critical for optimizing wastewater treatment processes and reducing operating costs and energy consumption. Due to their large size and numerous state variables, these wastewater treatment plants are considered as high-dimensional systems. The complexity of wastewater treatment plants results in varying and complex process noise statistics, posing challenges for state estimation. This paper proposes a novel state estimation method for wastewater treatment plants subject to inaccurate process noise statistics. The high-dimensional state vector is partitioned into multiple state blocks based on the system architecture, and lost correlations between blocks are compensated by considering time-series correlations. Real-time modification of the process noise covariance matrix is applied to adaptively adjust the inaccurate process noise statistics and compensate for errors from block division. It is verified through simulations that the proposed Bayesian algorithm can achieve satisfactory estimation results while the computational cost is moderate.

Robust Methods for Assessing the Characteristics of Locomotor Activity Based on Markerless Video Capture Data

Introduction. Analysis of locomotor activity is essential in a number of biomedical and pharmacological research designs, as well as environmental monitoring. The movement trajectories of biological objects can be represented by time series exhibiting a complex multicomponent structure and non-stationary dynamics, thus limiting the effectiveness of conventional correlation and spectral time series analysis methods. Recordings obtained using markerless technologies are typically characterized by enhanced noise levels, including both instrumental noise and anomalous errors associated with false estimates of the location of the points of interest, as well as gaps in the trajectories, promoting an urgent need in the development of robust methods to assess the characteristics of locomotor activity.Aim. Development of robust methods for assessing the characteristics of locomotor activity capable of efficient processing of noisy recordings obtained by markerless video-based motion capture systems.Materials and methods. In order to assess the characteristics of locomotor activity, the relative movements of body parts of laboratory animals were analyzed using the stability metrics of the mutual dynamics of their trajectories, their relative delays, as well as the relative duration of the recording fragments when relatively stable mutual dynamics could be observed. The local maxima of the cross-correlation function of two body fragments, the minima of the standard deviation of the difference between their Hilbert phases, as well as their relative delays, were used as the metrics of mutual dynamics.Results. The considered phase metrics were shown to explicitly reflect changes in locomotor activity, while the assessment of time delays using phase metric was shown to be prone to periodic error. The above limitation could be largely overcome using the correlation metrics, assuming that phase and correlation metrics could be combined.Conclusion. The proposed robust methods provide stable estimates of the characteristics of locomotor activity based on markerless video capture recordings, altogether increasing the efficiency of diagnostic procedures and assessment of the therapeutic effect during rehabilitation.

Eigenvector Centrality Mapping Reveals Volatility of Functional Brain Dynamics in Anti-NMDA Receptor Encephalitis

BackgroundAnti-NMDA receptor encephalitis (NMDARE) causes long-lasting cognitive deficits associated with altered functional connectivity. Eigenvector centrality (EC) mapping represents a powerful new method for data-driven voxelwise and time-resolved estimation of network importance—beyond changes in classical static functional connectivity. MethodsTo assess changes in functional brain network organization, we applied EC mapping in 73 patients with NMDARE and 73 matched healthy control participants. Areas with significant group differences were further investigated using 1) spatial clustering analyses, 2) time series correlation to assess synchronicity between the hippocampus and cortical brain regions, and 3) correlation with cognitive and clinical parameters. ResultsDynamic, time-resolved EC showed significantly higher variability in 13 cortical areas (familywise error p < .05) in patients with NMDARE compared with healthy control participants. Areas with dynamic EC group differences were spatially organized in centrality clusters resembling resting-state networks. Importantly, variability of dynamic EC in the frontotemporal cluster was associated with impaired verbal episodic memory in patients (r = −0.25, p = .037). EC synchronicity between the hippocampus and the medial prefrontal cortex was reduced in patients compared with healthy control participants (familywise error p < .05, tmax = 3.76) and associated with verbal episodic memory in patients (r = 0.28, p = .019). Static EC analyses showed group differences in only one brain region (left intracalcarine cortex). ConclusionsWidespread changes in network dynamics and reduced hippocampal-medial prefrontal synchronicity were associated with verbal episodic memory deficits and may thus represent a functional neural correlate of cognitive dysfunction in NMDARE. Importantly, dynamic EC detected substantially more network alterations than traditional static approaches, highlighting the potential of this method to explain long-term deficits in NMDARE.

A rotor bearing system fault diagnosis method based on FSASCA-VMD and GraphSAGE-SA

Abstract In complex environments, signals from rotor bearing systems can easily be drowned out by strong noise, leading to low fault diagnosis accuracy. In order to reduce noise and improve diagnostic accuracy, this paper proposes a rotor bearing system fault diagnosis method based on FSASCA-VMD (Future Search Algorithm based on Sine Cosine Algorithm-Variational Mode Decomposition) and GraphSAGE-SA (Graph SAmple and aggreGatE-Self Attention). First, the FSASCA optimization algorithm is used to determine two parameters in VMD. The best combination found is then input into VMD to decompose the original signal. Then, filter the IMF (Intrinsic Mode Function) components with high correlation to the original signal using cumulative percentage kurtosis. Reconstruct the filtered IMF components to complete signal denoising. Finally, this paper utilizes graph theory and time series correlation to uncover the hidden relationships within the data. Utilizing the Euclidean distance as the edge weight between nodes, a graph model is established based on the topological structure of the PathGraph, and a GraphSAGE-SA fault diagnosis framework is constructed. Utilizing a self-attention mechanism to aggregate nodes enhances the weight allocation of important information. The experimental results indicate that the method proposed in this paper can effectively remove most of the noise in the signal while preserving a significant amount of useful information. In rotor bearing system fault diagnosis, the diagnostic accuracies of this method for simulated and laboratory signals are 98.33% and 98.56%, respectively, surpassing those of other methods.&amp;#xD;

Optimizing User Experience: A Data-Driven Approach to Enhancing B2B Invoicing Efficiency across Multiple Platforms PT Pakar Digital Global

This study is a deep dive into applying data-driven decision-making strategies to enhance user experience and efficiency in B2B invoicing across multiple platforms at Paper.id. Given the fintech industry’s rapid evolution, maintaining a competitive edge requires constant innovation, particularly in user activation and retention within the first month of usage. This research employs a comprehensive data analysis framework, integrating Time Series Analysis, Descriptive Analysis, and Correlation Analysis methods to extract actionable insights from user data stored in MySQL databases. The study also incorporates strategic planning tools like SWOT and TOWS analysis to identify and implement UI/UX enhancements using the Agile Scrum methodology. The effectiveness of these interventions is evaluated through a robust post-analysis, comparing metrics before and after the implementation across mobile and desktop platforms. Results demonstrate a significant improvement in user activation and retention rates on mobile platforms, validating the efficacy of the applied strategies. This paper contributes valuable insights into optimizing user experience in a dynamic market, emphasizing a structured, iterative approach to achieving sustained user engagement and business growth.