Correlated Time Series Research Articles

Can a human sing with an unseen artificial partner? Coordination dynamics when singing with an unseen human or artificial partner

This study investigated whether a singer’s coordination patterns differ when singing with an unseen human partner versus an unseen artificial partner (VOCALOID 6 voice synthesis software). We used cross-correlation analysis to compare the correlation of the amplitude envelope time series between the partner’s and the participant’s singing voices. We also conducted a Granger causality test to determine whether the past amplitude envelope of the partner helps predict the future amplitude envelope of the participants, or if the reverse is true. We found more pronounced characteristics of anticipatory synchronization and increased similarity in the unfolding dynamics of the amplitude envelopes in the human-partner condition compared to the artificial-partner condition, despite the tempo fluctuations in the human-partner condition. The results suggested that subtle qualities of the human singing voice, possibly stemming from intrinsic dynamics of the human body, may contain information that enables human agents to align their singing behavior dynamics with a human partner.

LightCTS*: Lightweight Correlated Time Series Forecasting Enhanced With Model Distillation

LightCTS*: Lightweight Correlated Time Series Forecasting Enhanced With Model Distillation

Research on the Optimization and Development of Low Carbon Energy Economy from the Perspective of Water Conservancy Engineering

In order to explore the optimal development path of low-carbon energy economy in universities, this paper proposes a new method based on complex network theory to describe the global evolution and transformation characteristics of multivariate time series correlation patterns. In order to more intuitively see the impact of product extraction inputs as endogenous factors on economic growth, this article explores the relationship between economic growth and product extraction inputs by constructing a Hamiltonian function and using optimization methods. When considering whether the extraction input share of products with different extraction ratios is different, this article found the relationship between the total extraction input of products with different extraction ratios and the input share of green and low-carbon products, and analyzed consumers' preferences; Extractive investment of products under budget constraints and policy constraints. In addition, this article uses the dynamic equation of household utility function and environmental quality to prove that the extractive input of products not only promotes carbon reduction, but also has a positive effect on promoting economic growth. The simulation results show that the low-carbon economic development model based on energy efficiency proposed in this paper can effectively improve the development path of low-carbon energy economy.

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.

Feature-fused residual network for time series classification

In various fields such as healthcare and transportation, accurately classifying time series data can provide important support for decision-making. To further improve the accuracy of time series classification, we propose a Feature-fused Residual Network based on Multi-scale Signed Recurrence Plot (MSRP-FFRN). This method transforms one-dimensional time series into two-dimensional images, representing the temporal correlation of time series in a two-dimensional space and revealing hidden details within the data. To enhance these details further, we extract multi-scale features by setting receptive fields of different sizes and using adaptive network depths, which improves image quality. To evaluate the performance of this method, we conducted experiments on 43 UCR datasets and compared it with nine state-of-the-art baseline methods. The experimental results show that MSRP-FFRN ranks first on critical difference diagram, achieving the highest accuracy on 18 datasets with an average accuracy of 89.9%, making it the best-performing method overall. Additionally, the effectiveness of this method is further validated through metrics such as Precision, Recall, and F1 score. Results from ablation experiments also highlight the efficacy of the improvements made by MSRP-FFRN.

Pseudo-variance quasi-maximum likelihood estimation of semi-parametric time series models

We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian quasi-likelihood function and it relies on the specification of a parametric pseudo-variance that can contain parametric restrictions with respect to the conditional expectation. The specification of the pseudo-variance and the parametric restrictions follow naturally in observation-driven models with bounds in the support of the observable process, such as count processes and double-bounded time series. We derive the asymptotic properties of the estimators and a validity test for the parameter restrictions. We show that the results remain valid irrespective of the correct specification of the pseudo-variance. The key advantage of the restricted estimators is that they can achieve higher efficiency compared to alternative quasi-likelihood methods that are available in the literature. Furthermore, the testing approach can be used to build specification tests for parametric time series models. We illustrate the practical use of the methodology in a simulation study and two empirical applications featuring integer-valued autoregressive processes, where assumptions on the dispersion of the thinning operator are formally tested, and autoregressions for double-bounded data with application to a realized correlation time series.

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.

Social‐ATPGNN: Prediction of multi‐modal pedestrian trajectory of non‐homogeneous social interaction

AbstractWith the development of automatic driving and path planning technology, predicting the moving trajectory of pedestrians in dynamic scenes has become one of key and urgent technical problems. However, most of the existing techniques regard all pedestrians in the scene as equally important influence on the predicted pedestrian's trajectory, and the existing methods which use sequence‐based time‐series generative models to obtain the predicted trajectories, do not allow for parallel computation, it will introduce a significant computational overhead. A new social trajectory prediction network, Social‐ATPGNN which integrates both temporal information and spatial one based on ATPGNN is proposed. In space domain, the pedestrians in the predicted scene are formed into an undirected and non fully connected graph, which solves the problem of homogenisation of pedestrian relationships, then, the spatial interaction between pedestrians is encoded to improve the accuracy of modelling pedestrian social consciousness. After acquiring high‐level spatial data, the method uses Temporal Convolutional Network which could perform parallel calculations to capture the correlation of time series of pedestrian trajectories. Through a large number of experiments, the proposed model shows the superiority over the latest models on various pedestrian trajectory datasets.

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