Dynamic Time Series Research Articles

Online Learning of Temporal Association Rule on Dynamic Multivariate Time Series Data

Online Learning of Temporal Association Rule on Dynamic Multivariate Time Series Data

Research on Deep Learning Models for Traffic Flow Prediction

The issue of urban traffic congestion is becoming increasingly severe, highlighting the need for accurate traffic flow prediction to facilitate effective traffic management. Traditional prediction methods often struggle to address the complex spatiotemporal dependencies and external factors inherent in traffic data. This paper reviews existing deep learning models applied to traffic flow prediction, categorizing them into spatial and temporal types based on their dependencies. Spatial dependency models include those based on Euclidean space, such as CNN-based models, and non-Euclidean space models that combine Graph Convolutional Networks (GCN) with attention mechanism. These models effectively capture spatial variations in traffic flow data. Temporal dependency models, such as Recurrent Neural Network (RNN) and Temporal Graph Convolutional Network (T-GCN), focus on capturing long-term dependencies and time series dynamics. The selection of models depends on specific tasks and data characteristics. The article concludes with a summary and outlook on the entire discussion.

Understanding the temporal variability and predictability of streamflow signatures in the Colorado River Basin

It is well established that streamflow regimes evolve over decadal time scales (i.e., low frequency) leading to long term shifts in distributions. Similar low frequency variations have also been documented in streamflow predictability. Here we explore connections between streamflow distribution attributes and predictability regimes in the Upper Colorado River Basin. We employ nonlinear dynamical time series analysis methods on streamflow timeseries covering the period 762 – 2019 for six locations in the basin. First, a wavelet spectral analysis is performed to obtain the quasi-periodic ‘signal’ of the streamflow. The wavelet analysis also provides the temporal variability of the variance of the signal time series. The signal time series is embedded in a D-dimensional space with appropriate lag to reconstruct the phase space of the dynamics – i.e. the attractor. Overall predictability is assessed by quantifying the average divergence trajectories in the phase space using Global Lyapunov Exponents and the temporal variability of predictability via the Local Lyapunov Exponents. Results show clear oscillations in streamflow predictability with periods of both high and low predictability occurring throughout the study period at all gauges. Comparing predictability timeseries across the stream gauges we find that general consistency in high and low predictability periods, although they do not perfectly align temporally. In general, higher (lower) predictability periods are characterized by lower (higher) streamflow variance. While there is not a clear relationship between streamflow magnitude and predictability in general, modern high predictability epochs are characterized by a slightly greater likelihood of dry years and lower likelihood of wet years than other epochs. These findings indicate the potential for statistically significant differences in streamflow signatures between high and low predictability periods. Exploring these fundings further with potential connections to large-scale climate can be helpful in exploiting them for skillful short and medium term flow projections.

Time-series dynamics in symbiont communities of acroporid corals undergoing cold stress in winter

The bleaching of corals due to cold stress has been seldom studied compared with bleaching events resulting from heat stress. In this study, using a camera connected to an observatory system, we discovered an Acropora cytherea-like coral colony that underwent cold bleaching in winter at a depth of approximately 20 m in Okinawa, Japan. This main colony and 8 nearby colonies with similar morphological traits were selected for study, and their genetic lineages were identified. The dynamics in the symbiont communities associated with the coral colonies during 2015 and 2016 were determined by metabarcoding. Bleaching in the winter of 2015-2016 was less severe than that in the winters of 2013-2014 and 2014-2015, and water temperatures were higher in the winter of 2015-2016. Analyses of genetic markers revealed that the 9 studied colonies were A. cytherea and A. hyacinthus species complexes with multiple genetic lineages. The symbionts in the 9 colonies included 2 major defining intragenomic variants, C50a and C50c, which are related to Cladocopium C3. The ratio of symbiont genotypes in the 8 nearby colonies remained largely unaltered throughout the sampling period. Although the ratio changed continually in the bleached colony, the alterations were not related to the seasonal fluctuations in temperature. This study revealed that certain C3 strains can endure low temperatures in winter and suggests that different genetic strains within the same genus can exhibit physiological differences.

Development of a Mathematical Forecasting Model RUONIA

The article examines the time series of dynamics of the RUONIA indicator, the key rate of the Bank of Russia, money supply, inflation for the period from January 2010 to the present time. During the study, methods of correlation analysis were used, as well as time series analysis, multicollinearity was checked, and autocorrelation was identified. The developed model for forecasting the value of RUONIA is based on the value of the current key rate of the Bank of Russia, the dynamics of the money supply, as well as the previous value of RUONIA. The model allows you to “predict” the value of RUONIA in order to make more informed financial decisions.

Real-time ocean wave prediction in time domain with autoregression and echo state networks

This study evaluates the potential of applying echo state networks (ESN) and autoregression (AR) for dynamic time series prediction of free surface elevation for use in wave energy converters (WECs). The performance of these models is evaluated on time series data at different water depths and wave conditions, including both measured and simulated data with a focus on real-time prediction of ocean waves at a given location without resolving for the surrounding ocean surface, in other words, short-time single-point forecasting. The work presented includes training the models on historical wave data and testing their ability to predict phase-resolved future surface wave patterns for short-time forecasts. Additionally, this study discusses the feasibility of deploying these models for extended time intervals. It provides valuable insights into the trade-offs between accuracy and practicality in the real-time implementation of predictive models for wave elevation, which are needed in wave energy converters to optimise the control algorithm.

Consistent causal inference for high-dimensional time series

A methodology for high-dimensional causal inference in a time series context is introduced. Time series dynamics are captured by a Gaussian copula, and estimation of the marginal distribution of the data is not required. The procedure can consistently identify the parameters that describe the dynamics of the process and the conditional causal relations among the possibly high-dimensional variables, under sparsity conditions. Identification of the causal relations is in the form of a directed acyclic graph, which is equivalent to identifying the structural VAR model for the transformed variables. As illustrative applications, we consider the impact of supply-side oil shocks on the economy and the causal relations between aggregated variables constructed from the limit order book for four stock constituents of the S&P500.

MNPM: research on metabolic neural network prediction model for predicting carbon emission accuracy

Abstract The rapid development of the global economy and society relies on continuous energy demand, while the severe impact of carbon emissions on the ecological environment has garnered significant international attention. Accurately forecasting carbon emission trends is crucial for developing effective reduction strategies and ensuring sustainable green economic development. In this paper, we propose a Metabolic Neural Network Prediction Model (MNPM) for carbon emissions. This model comprehensively considers the impact of various carbon emission-related factors across different regions in China. By employing one-hot encoding, we address the difficulties traditional classifiers face when handling categorical data, enabling predictions under more realistic conditions. To optimize the nonlinear characteristics of the data and overcome the limitations of grey models, we utilize dynamic iterative time series training to address errors due to data inaccuracies effectively. Experimental results demonstrate that our approach outperforms other methods in filtering out irrelevant data, achieving an average relative residual of 0.055 and an average ratio bias of 0.049, translating to more precise prediction accuracy.

Distance similarity entropy: a sensitive nonlinear feature extraction method for rolling bearing fault diagnosis

Entropy-based methods are widely used in machinery fault diagnosis for characterizing system disorder and complexity. However, conventional entropy techniques often fail to capture local signal variations when analyzing relationships between vectors, especially in complex settings. This leads to incomplete representations of subtle features and dynamic behaviors, resulting in inaccurate estimations of system complexity and affecting diagnostic accuracy and reliability. To address these limitations, a novel distance similarity entropy (DSEn) is proposed in this paper: (1) It leverages element-wise distances to precisely capture local shifts and subtle distortions between subsequences. (2) It employs a Gaussian kernel function for vector similarity, enhancing signal pattern analysis by preserving subtle differences and mitigating the impact of outliers. (3) It uses probability density estimation of distance similarities between adjacent vectors to track changes in internal signal patterns, enabling more accurate and sensitive estimations of signal complexity. Synthetic signal experiments demonstrate that DSEn excels in detecting dynamic time series changes and characterizing signal complexity. Tests on two bearing datasets reveal that DSEn's extracted features show significant differences, highlighted by Hedges’ g effect size. Compared to other commonly used entropies (SampEn, PermEn, FuzzEn, DistEn, etc.), DSEn shows superior fault identification accuracy, computational efficiency, and noise resistance.

Modeling Ordinal First Return Dynamics from Time Series

We examine the family of ordinal First Return Maps (FRMs) of a dynamical system time series to model the system’s dynamics. We consider two distinct modeling approaches using the same modeling method and compare their outcomes to ascertain the prerequisites for each to function and which approach is more effective in different circumstances. The first approach involves short-term modeling of the entire flow, followed by identifying the ordinal sections on the predicted flow. The second approach relies on locating the ordinal sections within the reference time series and using the data from each section independently to build a model that can produce a long-term prediction for each section’s FRM. We demonstrate the effectiveness of these approaches on two well-known dynamical systems, the Lorenz and Rössler equations, emulating data deficiency by selecting a low sampling rate. We consider the effect of downsampling on the shape of the FRMs to choose suitable ordinal sequences to use in creating Poincaré sections from the time series. Following that, we propose a dissimilarity measure between the reference and predicted FRMs to assess the model quality. We then compare the reference and predicted FRMs using the introduced dissimilarity criterion to determine which modeling approach performs better in each situation. Ultimately, we classify the FRMs situation into continuous and piecewise continuous scenarios. Based on our observations from the Lorenz and Rössler dynamical systems, we found that when the system’s FRMs are piecewise continuous, it is more effective to model the entire flow. However, when the FRMs are continuous, our choice of modeling approach depends on the criterion that the predicted FRM is more similar to the reference.

Application of graph-structured data for forecasting the dynamics of time series of natural origin

Application of graph-structured data for forecasting the dynamics of time series of natural origin

Enhanced Wavelet Transform Dynamic Attention Transformer Model for Recycled Lithium-Ion Battery Anomaly Detection

Rapid advancements in electric vehicle (EV) technology have highlighted the importance of lithium-ion (Li) batteries. These batteries are essential for safety and reliability. Battery data show non-stationarity and complex dynamics, presenting challenges for current monitoring and prediction methods. These methods often fail to manage the variability seen in real-world environments. To address these challenges, we propose a Transformer model with a wavelet transform dynamic attention mechanism (WADT). The dynamic attention mechanism uses wavelet transform. It focuses adaptively on the most informative parts of the battery data to enhance the anomaly detection accuracy. We also developed a deep learning model with an improved Transformer architecture. This architecture is tailored for the complex dynamics of battery data time series. The model accounts for temporal dependencies and adapts to non-stationary behavior. Experiments on public battery datasets show our approach’s effectiveness. Our model significantly outperforms existing technologies with an accuracy of 0.89 and an AUC score of 0.88. These results validate our method’s innovation and effectiveness.

Lagged multidimensional recurrence quantification analysis for determining leader-follower relationships within multidimensional time series.

The current article introduces lagged multidimensional recurrence quantification analysis. The method is an extension of multidimensional recurrence quantification analysis and allows to quantify the joint dynamics of multivariate time series and to investigate leader-follower relationships in behavioral and physiological data. Moreover, the method enables the quantification of the joint dynamics of a group, when such leader-follower relationships are taken into account. We first provide a formal presentation of the method, and then apply it to synthetic data, as well as data sets from joint action research, investigating the shared dynamics of facial expression and beats-per-minute recordings within different groups. A wrapper function is included, for applying the method together with the "crqa" package in R. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

A novel HMM distance measure with state alignment

In this paper, we introduce a novel distance measure that conforms to the definition of a semi-distance, for quantifying the similarity between Hidden Markov Models (HMMs). This distance measure is not only easier to implement, but also accounts for state alignment before distance calculation, ensuring correctness and accuracy. Our proposed distance measure presents a significant advancement in HMM comparison, offering a more practical and accurate solution compared to existing measures. Numerical examples that demonstrate the utility of the proposed distance measure are given for HMMs with continuous state probability densities. In real-world data experiments, we employ HMM to represent the evolution of financial time series or music. Subsequently, leveraging the proposed distance measure, we conduct HMM-based unsupervised clustering, demonstrating promising results. Our approach proves effective in capturing the inherent difference in dynamics of financial time series, showcasing the practicality and success of the proposed distance measure.

The Painful Double-Knock on Food Prices: 2008 Financial Crises and COVID-19 Pandemic

Food supply and demand chains are susceptible to global shocks. Unstable and sudden food price hikes cause serious malnutrition problems and increase the number of food-insecure people, especially in developing countries. Using the FAO Food Price Index (FFPI), this study makes one of the first attempts to utilize monthly observations of the FFPI in dynamic time series ARDL and ARX settings to identify the effects of food prices on COVID-19 infection rates and the 2008 global financial crisis. Our empirical findings confirm that the financial crisis significantly increased the FFPI, although its effects decreased as markets equilibrated between 2007 and 2009. The pandemic has had a mild impact on food prices in the short run compared to the 2008 crisis, but in the long run, the COVID-19 outbreak has a larger impact, with 1 million new COVID-19 infections associated with an increase of between 0.0464 and 0.0509 points in the FFPI. Food price volatility and hikes, even if short-term, increase poverty, malnutrition, and food insecurity, foster social unrest, and lower people’s living standards. This research implies that food prices are globally sensitive to both pandemics and financial crises, and the severity of the pandemic can drive global food prices higher, depending on the number of infections. Over the long run, the impact of the outbreak surpasses that of the financial crisis. The latter tends to have a major impact on food prices in the short run but subsequently declines as markets begin to equilibrate, reflecting asymmetries between the two phenomena in their effects on food prices. Overall, the results indicate that the financial crisis and the COVID-19 pandemic had a short-run, immediate, augmenting impact on food prices. However, while the 2008 crisis affected the supply side only, COVID-19 had impacts on both the demand and supply sides.

Zoonotic outbreak risk prediction with long short-term memory models: a case study with schistosomiasis, echinococcosis, and leptospirosis

BackgroundZoonotic infections, characterized with huge pathogen diversity, wide affecting area and great society harm, have become a major global public health problem. Early and accurate prediction of their outbreaks is crucial for disease control. The aim of this study was to develop zoonotic diseases risk predictive models based on time-series incidence data and three zoonotic diseases in mainland China were employed as cases.MethodsThe incidence data for schistosomiasis, echinococcosis, and leptospirosis were downloaded from the Scientific Data Centre of the National Ministry of Health of China, and were processed by interpolation, dynamic curve reconstruction and time series decomposition. Data were decomposed into three distinct components: the trend component, the seasonal component, and the residual component. The trend component was used as input to construct the Long Short-Term Memory (LSTM) prediction model, while the seasonal component was used in the comparison of the periods and amplitudes. Finaly, the accuracy of the hybrid LSTM prediction model was comprehensive evaluated.ResultsThis study employed trend series of incidence numbers and incidence rates of three zoonotic diseases for modeling. The prediction results of the model showed that the predicted incidence number and incidence rate were very close to the real incidence data. Model evaluation revealed that the prediction error of the hybrid LSTM model was smaller than that of the single LSTM. Thus, these results demonstrate that using trending sequences as input sequences for the model leads to better-fitting predictive models.ConclusionsOur study successfully developed LSTM hybrid models for disease outbreak risk prediction using three zoonotic diseases as case studies. We demonstrate that the LSTM, when combined with time series decomposition, delivers more accurate results compared to conventional LSTM models using the raw data series. Disease outbreak trends can be predicted more accurately using hybrid models.

New parameterization of stochastic conditional range models for financial volatility modelling

The financial market returns and daily range data often exhibit asymmetry and peak around the mean with heavier tails than normal distribution. To analyze the volatility dynamics of these financial time series using stochastic conditional range (SCR) models, the choice of conditional distribution for innovations has posed challenges. A suitably chosen distribution, which can capture stylized facts inherent in these data, particularly excess kurtosis, has been proven to be very useful. This study introduces a new parameterization for SCR models using an extended generalized inverse Gaussian distribution to incorporate the flexibility of choice of various marginal distributions to the innovations of the model. We discuss the theoretical properties of the proposed models and develop a maximum likelihood method based on efficient importance sampling to estimate the parameters of the proposed SCR models. The simulation results showed that the proposed estimation methodology performs well. Finally, the proposed models were used to analyze real datasets.

A novel optimal temporal lag air2stream model using dynamic time series matching

ABSTRACT In order to solve the problem that the current air2stream model does not consider the lag change of water temperature, this paper proposes a new method that combines empirical mode decomposition, power spectral density and dynamic time warping algorithm to determine the optimal time lag parameters, and then constructs the air2stream with the optimal time lag (a2swtl). Finally, the effectiveness and stability of the new method and model were verified based on the measured data from 2020-2022 at three hydrological stations in the middle and lower reaches of the Yangtze River that are close to natural river conditions. The results show that the new method overcomes the problem of low accuracy in determining the time lag of the existing correlation coefficient method. Compared with the original model, a2swtl has better stability without introducing additional observation data, and the average prediction accuracy is improved by about 6.33%. 8.36% and 15.4%.

Dynamic convolutional time series forecasting based on adaptive temporal bilateral filtering

Time series data typically contain complex dynamic patterns, which not only include linear trends and seasonal variations but also significant nonlinear changes and complex dependencies. Currently, feature extraction methods for time series data primarily employ mixed-mode extraction within the temporal domain, neglecting the effective extraction and analysis of nonlinear characteristics between different observation points and the interdependencies between variables. To address these issues, we designed an adaptive temporal bilateral filtering module that effectively preserves and highlights the nonlinear features and patterns in time series while filtering out noise and redundant information. We also designed a nonlinear feature adaptive extraction module that integrates a gating mechanism and deformable convolutions. This design allows the model to adaptively adjust the shape of the convolutional kernels according to different time steps and conditions. This enables accurate capture and extraction of nonlinear features between various time observations and dependencies between different variables. Additionally, we use stacked convolutional layers to extract local contextual features, addressing fluctuations in local features caused by changes in data distribution in real-world scenarios. In summary, we propose DCNet, a dynamic convolutional network based on an adaptive temporal bilateral filter, and evaluated its performance on twelve real-world datasets. The results indicate that DCNet consistently achieves state-of-the-art performance in both short-term and long-term forecasting tasks, with favorable runtime efficiency.

Identifying chaotic dynamics in noisy time series through multimodal deep neural networks

Abstract Chaos detection is the problem of identifying whether a series of measurements is being sampled from an underlying set of chaotic dynamics. The unavoidable presence of measurement noise significantly affects the performance of chaos detectors, as discerning chaotic dynamics from stochastic signals becomes more challenging. This paper presents a computationally efficient multi-modal deep neural network tailored for chaos detection by combining information coming from the analysis of time series, recurrence plots and spectrograms. The proposed approach is the first one suitable for multi-class classification of chaotic systems while being robust with respect to measurement noise, and is validated on a dataset of 15 different chaotic and non-chaotic dynamics subject to white, pink or brown coloured noise.