Real Time Series Research Articles

An efficient improved singular spectrum analysis for processing GNSS position time series with missing data

Summary The improved SSA (ISSA) method is widely recognized for directly extracting signals from gappy time series without requiring prior interpolation. However, it is rather time consuming, particularly for long time series with large window sizes, such as Global Navigation Satellite System (GNSS) position time series. This study proposes an efficient ISSA method that yields equivalent results to the ISSA method while significantly reducing computation time. Both methods aim to minimize the quadratic norm of principal components, while our method has fewer unknown parameters in the principal component computation than those of the ISSA method. We evaluate the performance of the proposed method using real GNSS position time series from 27 permanent stations located in mainland China. Results show that the proposed method can effectively reduce computation time than the ISSA method and the improvement depends on the chosen window size, the time series length, and the percentage of missing data. This efficient approach can be naturally extended to principal component analysis (PCA) and multi-channel SSA (MSSA) for processing multiple incomplete time series, improving computational efficiencies compared to the modified PCA and the improved MSSA while maintaining unchanged results. We also compare the ISSA method with the modified SSA (SSAM) and the iterative SSA methods using both real and synthetic time series data. Results indicate that the ISSA method outperforms the SSAM method, and when conducted iteratively, also surpasses the iterative SSA method.

SINGULAR SPECTRAL ANALYSIS OF TEMPERATURE MULTIDIMENSIONAL TIME SERIES

In the paper the algorithm of singular structural analysis and forecasting of a multidimensional series by the MSSA method is used. The program was developed, in which the steps of the method for the selection of singular decomposition components were implemented, the analysis and forecast of real time series was carried out. Singular spectrum analysis (SSA) is increasingly used in the study of time series. Unlike other methods of statistical research of time series, this method is used to study the structure, selection of individual components and forecast of both stationary and non-stationary time series. It does not require an analytical model of the series. In fact, this approach is based on the method of principal components. It is based on the transformation of a series into a matrix and its singular decomposition. After identifying the components of the singular decomposition, their grouping takes place, which leads to the decomposition of the original series into additive components, such as trend, oscillations (periodics), and noise. The SSA method allows you to continue the structure of the time series, thus building a forecast (continuation). An important direction of the development of the SSA method as a method of time series analysis is its generalization for the analysis of multidimensional time series. The method is known as MSSA (Multi-Channel SSA) or E-EOFs (Extended Empirical Orthogonal Functions). In this case, the expected result is the simultaneous decomposition of several series into interpreted components. However, a sufficiently complete theory for MSSA does not exist.

Polynomial fuzzy information granule based [formula omitted]-triple I fuzzy reasoning algorithm and its short-term forecasting of time series

Short-term forecasting of time series is an important research topic, which involves data characteristic capture and intelligent reasoning. For this topic, the Gaussian polynomial fuzzy information granule with interpretability is granulated on data, enabling the extraction of data trend characteristic, besides, the associate characteristic within the data is captured through building fuzzy association rule. Building upon the data characteristics captured in fuzzy information granule and fuzzy association rule, an intelligent reasoning algorithm called the fuzzy information granule based α-Triple I algorithm is proposed, where the membership degree of data to granule is considered in reasoning, and next the accurate level of deviation from data to granule can be inferenced. Based on the excavated data characteristics and a rational inference, a short-term forecasting model is established. Its superiority in terms of accuracy and reliability when compared to 7 other models in real time series has been tested. Notably, the prediction of the novel model is accurate because the function of FAR is identified from FAR’s truth degree, which means the validity degree of prediction. The application of the proposed model for short-term forecasting holds a potential impact across various fields.

Reliable generation of privacy-preserving synthetic electronic health record time series via diffusion models.

Electronic health records (EHRs) are rich sources of patient-level data, offering valuable resources for medical data analysis. However, privacy concerns often restrict access to EHRs, hindering downstream analysis. Current EHR deidentification methods are flawed and can lead to potential privacy leakage. Additionally, existing publicly available EHR databases are limited, preventing the advancement of medical research using EHR. This study aims to overcome these challenges by generating realistic and privacy-preserving synthetic EHRs time series efficiently. We introduce a new method for generating diverse and realistic synthetic EHR time series data using denoizing diffusion probabilistic models. We conducted experiments on 6 databases: Medical Information Mart for Intensive Care III and IV, the eICU Collaborative Research Database (eICU), and non-EHR datasets on Stocks and Energy. We compared our proposed method with 8 existing methods. Our results demonstrate that our approach significantly outperforms all existing methods in terms of data fidelity while requiring less training effort. Additionally, data generated by our method yield a lower discriminative accuracy compared to other baseline methods, indicating the proposed method can generate data with less privacy risk. The proposed model utilizes a mixed diffusion process to generate realistic synthetic EHR samples that protect patient privacy. This method could be useful in tackling data availability issues in the field of healthcare by reducing barrier to EHR access and supporting research in machine learning for health. The proposed diffusion model-based method can reliably and efficiently generate synthetic EHR time series, which facilitates the downstream medical data analysis. Our numerical results show the superiority of the proposed method over all other existing methods.

Variational inference of single cell time series.

Time course single-cell RNA sequencing (scRNA-seq) enables researchers to probe genome-wide expression dynamics at the the single cell scale. However, when gene expression is affected jointly by time and cellular identity, analyzing such data - including conducting cell type annotation and modeling cell type-dependent dynamics - becomes challenging. To address this problem, we propose SNOW (SiNgle cell flOW map), a deep learning algorithm to deconvolve single cell time series data into time-dependent and time-independent contributions. SNOW has a number of advantages. First, it enables cell type annotation based on the time-independent dimensions. Second, it yields a probabilistic model that can be used to discriminate between biological temporal variation and batch effects contaminating individual timepoints, and provides an approach to mitigate batch effects. Finally, it is capable of projecting cells forward and backward in time, yielding time series at the individual cell level. This enables gene expression dynamics to be studied without the need for clustering or pseudobulking, which can be error prone and result in information loss. We describe our probabilistic framework in detail and demonstrate SNOW using data from three distinct time course scRNA-seq studies. Our results show that SNOW is able to construct biologically meaningful latent spaces, remove batch effects, and generate realistic time-series at the single-cell level. By way of example, we illustrate how the latter may be used to enhance the detection of cell type-specific circadian gene expression rhythms, and may be readily extended to other time-series analyses.

Generating realistic neurophysiological time series with denoising diffusion probabilistic models

Generating realistic neurophysiological time series with denoising diffusion probabilistic models

Single molecule dynamics in a virtual cell combining a 3-dimensional matrix model with random walks

Recent advances in light microscopy have enabled single molecules to be imaged and tracked within living cells and this approach is impacting our understanding of cell biology. Computer modeling and simulation are important adjuncts to the experimental cycle since they aid interpretation of experimental results and help refine, test and generate hypotheses. Object-oriented computer modeling is particularly well-suited for simulating random, thermal, movements of individual molecules as they interact with other molecules and subcellular structures, but current models are often limited to idealized systems consisting of unit volumes or planar surfaces. Here, a simulation tool is described that combines a 3-dimensional, voxelated, representation of the cell consisting of subcellular structures (e.g. nucleus, endoplasmic reticulum, cytoskeleton, vesicles, and filopodia) combined with numerical floating-point precision simulation of thousands of individual molecules moving and interacting within the 3-dimensional space. Simulations produce realistic time-series video sequences comprising single fluorophore intensities and realistic background noise which can be directly compared to experimental fluorescence video microscopy data sets.

Applying (ARFIMA) Model for Forecast the Saudi Stock Market Prices

The interest in the topic of time series forecasting has increased during the recent years and thus appeared specific modern methods, for example Autoregressive Fractional Integrated Moving Average model (ARFIMA), or what is called long memory model, which use fractionally difference (d) instead of integer which used in ARIMA models. In this study we displayed long memory feature and its tests. Our discussion supported by analysing the real time series (daily closing index of the Saudi Arabia Stock Market prices) over period 1/1/2018 to 19/12/2022, including 1240 observations, to make a good model to giving forecast results for future, using statistical tests and statistical software (R- 4.2.2 program). Firstly we checked that the data series was unstable by testing unit root, using Dickey fuller and Philips Perron tests ; and confirmed the presence of a long memory pattern in it by calculating the Hurst exponent (H), then calculated the fractional differential coefficient (d), determined the appropriate models for analysis and prediction, then the best model was chosen among them based on the comparison criteria, then predicted the values for the next 5 days, R - 4.2.2 software was used in all of these tests and predictions Statistical results indicated that the optimal model to represent the data series is ARFIMA (3,0.383,2) which used to predict future values.

General estimation results for tdVARMA array models

The article will focus on vector autoregressive‐moving average (VARMA) models with time‐dependent coefficients (td) to represent general nonstationary time series, not necessarily Gaussian. The coefficients depend on time, possibly on the length of the series , hence the name tdVARMA for the models, but not necessarily on the rescaled time . As a consequence of the dependency on of the model, we need to consider array processes instead of stochastic processes. Under appropriate assumptions, it is shown that a Gaussian quasi‐maximum likelihood estimator is consistent in probability and asymptotically normal. The theoretical results are illustrated using three examples of bivariate processes, the first two with marginal heteroscedasticity. The first example is a tdVAR(1) process while the second example is a tdVMA(1) process. In these two cases, the finite‐sample behavior is checked via a Monte Carlo simulation study. The results are compatible with the asymptotic properties even for small . A third example shows the application of the tdVARMA models for a real time series.

A Meta-learner approach to multistep-ahead time series prediction

AbstractThe utilization of machine learning has become ubiquitous in addressing contemporary challenges in data science. Moreover, there has been significant interest in democratizing the decision-making process for selecting machine learning algorithms, achieved through the incorporation of meta-features and automated machine learning techniques for both classification and regression tasks. However, this paradigm has not been readily applied to multistep-ahead time series prediction problems. Unlike regression and classification problems, which utilize independent variables not derived from the target variable, time series models typically rely on past values of the series to forecast future outcomes. The structure of a time series is often characterized by features such as trend, seasonality, cyclicality and irregularity. In our study, we illustrate how time series metrics representing these features, in conjunction with an ensemble-based regression Meta-Learner, were employed to predict the standardized mean square error of candidate time series prediction models. Our experiments utilized datasets covering a broad feature space, facilitating the selection of the most effective model by researchers. A rigorous evaluation was conducted to assess the performance of the Meta-Learner on both synthetic and real time series data.

Phase coherence-A time-localized approach to studying interactions.

Coherence measures the similarity of progression of phases between oscillations or waves. When applied to multi-scale, nonstationary dynamics with time-varying amplitudes and frequencies, high values of coherence provide a useful indication of interactions, which might otherwise go unnoticed. However, the choice of analyzing coherence based on phases and amplitudes (amplitude-weighted phase coherence) vs only phases (phase coherence) has long been seen as arbitrary. Here, we review the concept of coherence and focus on time-localized methods of analysis, considering both phase coherence and amplitude-weighted phase coherence. We discuss the importance of using time-localized analysis and illustrate the methods and their practicalities on both numerically modeled and real time-series. The results show that phase coherence is more robust than amplitude-weighted phase coherence to both noise perturbations and movement artifacts. The results also have wider implications for the analysis of real data and the interpretation of physical systems.

DiffPLF: A conditional diffusion model for probabilistic forecasting of EV charging load

Due to the vast electric vehicle (EV) penetration to distribution grid, charging load forecasting is essential to promote charging station operation and demand-side management. However, the stochastic charging behaviors and associated exogenous factors render future charging load patterns quite volatile and hard to predict. Accordingly, we devise a novel Diffusion model termed DiffPLF for Probabilistic Load Forecasting of EV charging, which can explicitly approximate the predictive load distribution conditioned on historical data and related covariates. Specifically, we leverage a denoising diffusion model, which can progressively convert the Gaussian prior to real time-series data by learning a reversal of the diffusion process. Besides, we couple such diffusion model with a cross-attention-based conditioning mechanism to execute conditional generation for possible charging demand profiles. We also propose a task-informed fine-tuning technique to better adapt DiffPLF to the probabilistic time-series forecasting task and acquire more accurate and reliable predicted intervals. Finally, we conduct multiple experiments to validate the superiority of DiffPLF to predict complex temporal patterns of erratic charging load and carry out controllable generation based on certain covariate. Results demonstrate that we can attain a notable rise of 39.58% and 49.87% on MAE and CRPS respectively compared to the conventional method.

ECG-Image-Kit: a synthetic image generation toolbox to facilitate deep learning-based electrocardiogram digitization

Objective. Cardiovascular diseases are a major cause of mortality globally, and electrocardiograms (ECGs) are crucial for diagnosing them. Traditionally, ECGs are stored in printed formats. However, these printouts, even when scanned, are incompatible with advanced ECG diagnosis software that require time-series data. Digitizing ECG images is vital for training machine learning models in ECG diagnosis, leveraging the extensive global archives collected over decades. Deep learning models for image processing are promising in this regard, although the lack of clinical ECG archives with reference time-series data is challenging. Data augmentation techniques using realistic generative data models provide a solution. Approach. We introduce ECG-Image-Kit, an open-source toolbox for generating synthetic multi-lead ECG images with realistic artifacts from time-series data, aimed at automating the conversion of scanned ECG images to ECG data points. The tool synthesizes ECG images from real time-series data, applying distortions like text artifacts, wrinkles, and creases on a standard ECG paper background. Main results. As a case study, we used ECG-Image-Kit to create a dataset of 21 801 ECG images from the PhysioNet QT database. We developed and trained a combination of a traditional computer vision and deep neural network model on this dataset to convert synthetic images into time-series data for evaluation. We assessed digitization quality by calculating the signal-to-noise ratio and compared clinical parameters like QRS width, RR, and QT intervals recovered from this pipeline, with the ground truth extracted from ECG time-series. The results show that this deep learning pipeline accurately digitizes paper ECGs, maintaining clinical parameters, and highlights a generative approach to digitization. Significance. The toolbox has broad applications, including model development for ECG image digitization and classification. The toolbox currently supports data augmentation for the 2024 PhysioNet Challenge, focusing on digitizing and classifying paper ECG images.

A novel outlier detection method based on Bayesian change point analysis and Hampel identifier for GNSS coordinate time series

The identification and removal of outliers in time series are important problems in numerous fields. In this paper, a novel method (BCP-HI) is proposed to enhance the accuracy of outlier detection in GNSS coordinate time series by combining Bayesian change point (BCP) analysis and the Hampel identifier (HI). By using BCP, change points (cps) in the time series are lidentified, and so the time series is divided into subsegments that have properties of a normal distribution. In each of these separated segments, outliers are detected using HI. Each data element identified as an outlier is corrected by a median filter of window size (w) to obtain the corrected signal. The BCP-HI method was tested on both simulated and real GNSS coordinate time series. Outliers from three different synthetic test datasets with different sampling frequencies and outlier amplitudes were detected with approximately 98% accuracy after processing. After this process, Signal-to-Noise Ratio (SNR) increased from 0.0084 to 10.8714 dB and Root Mean Square (RMS) decreased from 24 to 23 mm. Similarly, for real GNSS data, approximately 98% accuracy was achieved, with an increase in SNR from 0.0003 to 4.4082 dB and a decrease in RMS from 7.6 to 6.6 mm observed. In addition, the output signals after BCP-HI were examined graphically using Lomb–Scargle periodograms and it was observed that clearer power spectrum distributions emerged. When the input and output signals were examined using the Kolmogorov–Smirnov (KS) test, they were found to be statistically similar. These results indicate that the BCP-HI algorithm effectively removes outliers, and enhances processing accuracy and reliability, and improves signal quality.

Generating Synthetic Electricity Load Time Series at District Scale Using Probabilistic Forecasts

Thanks to various European directives, individuals are empowered to share and trade electricity within Renewable Energy Communities, enhancing the operational efficiency of local energy systems. The digital transformation of the energy market enables the integration of decentralized energy resources using cloud computing, the Internet of Things, and artificial intelligence. In order to assess the feasibility of new business models based on data-driven solutions, various electricity consumption time series are necessary at this level of aggregation. Since these are currently not yet available in sufficient quality and quantity, and due to data privacy reasons, synthetic time series are essential in the strategic planning of smart grid energy systems. By enabling the simulation of diverse scenarios, they facilitate the integration of new technologies and the development of effective demand response strategies. Moreover, they provide valuable data for assessing novel load forecasting methodologies that are essential to manage energy efficiently and to ensure grid stability. Therefore, this research proposes a methodology to synthesize electricity consumption time series by applying the Box–Jenkins method, an intelligent sampling technique for data augmentation and a probabilistic forecast model. This novel approach emulates the stochastic nature of electricity consumption time series and synthesizes realistic ones of Renewable Energy Communities concerning seasonal as well as short-term variations and stochasticity. Comparing autocorrelations, distributions of values, and principle components of daily sequences between real and synthetic time series, the results exhibit nearly identical characteristics to the original data and, thus, are usable in designing and studying efficient smart grid systems.

Cumulative Difference Learning VAE for Time-Series with Temporally Correlated Inflow-Outflow

Time-series generation has crucial practical significance for decision-making under uncertainty. Existing methods have various limitations like accumulating errors over time, significantly impacting downstream tasks. We develop a novel generation method, DT-VAE, that incorporates generalizable domain knowledge, is mathematically justified, and significantly outperforms existing methods by mitigating error accumulation through a cumulative difference learning mechanism. We evaluate the performance of DT-VAE on several downstream tasks using both semi-synthetic and real time-series datasets, including benchmark datasets and our newly curated COVID-19 hospitalization datasets. The COVID-19 datasets enrich existing resources for time-series analysis. Additionally, we introduce Diverse Trend Preserving (DTP), a time-series clustering-based evaluation for direct and interpretable assessments of generated samples, serving as a valuable tool for evaluating time-series generative models.

Hierarchical organization of human physical activity

Human physical activity (HPA), a fundamental physiological signal characteristic of bodily motion is of rapidly growing interest in multidisciplinary research. Here we report the existence of hitherto unidentified hierarchical levels in the temporal organization of HPA on the ultradian scale: on the minute's scale, passive periods are followed by activity bursts of similar intensity (‘quanta’) that are organized into superstructures on the hours- and on the daily scale. The time course of HPA can be considered a stochastic, quasi-binary process, where quanta, assigned to task-oriented actions are organized into work packages on higher levels of hierarchy. In order to grasp the essence of this complex dynamic behaviour, we established a stochastic mathematical model which could reproduce the main statistical features of real activity time series. The results are expected to provide important data for developing novel behavioural models and advancing the diagnostics of neurological or psychiatric diseases.

Data-augmented landslide displacement prediction using generative adversarial network

Landslides are destructive natural disasters that cause catastrophic damage and loss of life worldwide. Accurately predicting landslide displacement enables effective early warning and risk management. However, the limited availability of on-site measurement data has been a substantial obstacle in developing data-driven models, such as state-of-the-art machine learning (ML) models. To address these challenges, this study proposes a data augmentation framework that uses generative adversarial networks (GANs), a recent advance in generative artificial intelligence (AI), to improve the accuracy of landslide displacement prediction. The framework provides effective data augmentation to enhance limited datasets. A recurrent GAN model, RGAN-LS, is proposed, specifically designed to generate realistic synthetic multivariate time series that mimics the characteristics of real landslide on-site measurement data. A customized moment-matching loss is incorporated in addition to the adversarial loss in GAN during the training of RGAN-LS to capture the temporal dynamics and correlations in real time series data. Then, the synthetic data generated by RGAN-LS is used to enhance the training of long short-term memory (LSTM) networks and particle swarm optimization-support vector machine (PSO-SVM) models for landslide displacement prediction tasks. Results on two landslides in the Three Gorges Reservoir (TGR) region show a significant improvement in LSTM model prediction performance when trained on augmented data. For instance, in the case of the Baishuihe landslide, the average root mean square error (RMSE) increases by 16.11%, and the mean absolute error (MAE) by 17.59%. More importantly, the model's responsiveness during mutational stages is enhanced for early warning purposes. However, the results have shown that the static PSO-SVM model only sees marginal gains compared to recurrent models such as LSTM. Further analysis indicates that an optimal synthetic-to-real data ratio (50% on the illustration cases) maximizes the improvements. This also demonstrates the robustness and effectiveness of supplementing training data for dynamic models to obtain better results. By using the powerful generative AI approach, RGAN-LS can generate high-fidelity synthetic landslide data. This is critical for improving the performance of advanced ML models in predicting landslide displacement, particularly when there are limited training data. Additionally, this approach has the potential to expand the use of generative AI in geohazard risk management and other research areas.

Empirical Evaluation of the Time Series Forecasting Method by Combining ARIMA with RBFNN under the Additive Model

Time series data is a series of values observed through repeated measurements at different times. Time series data is a type of data present in almost all different fields of life. Time series prediction is an significant problem in time series data mining. Accurate forecasting is crucial to support decision making in many areas of life. Therefore, improving the precision of time series predicting is a interesting mission for experts in this field. Many models for predicting time series have been proposed from traditional time series models as Auto Regressive Integrated Moving Average (ARIMA) model to artificial neural network (ANN) models. ARIMA is a linear model therefore it can only take the linear characteristics in time series. In contrast, Radial Basis Function Neural Network (RBFNN) is a non-linear model therefore it can not predict effectively seasonal or trend changes in time series. To combine the strengths of these two models, in this study, we experimentally evaluate the hybrid method between ARIMA and RBFNN on real time series data from different fields. Experimental results demonstrate that the combined method outperforms each model used individually in terms of accuracy.

Application of wavelet transformation and singular spectral analysis in time series decomposition

When studying a time series, it is traditionally customary to use a generalized mathematical model where a trend component, a cyclic component that describes the repeatability of a cyclic process over time intervals and a random component or noise – this component is responsible for factors hidden from the observer. It is assumed that the main trend and the cyclical component can be accurately described because they are formed by known factors that can be taken into account within the framework of models. The discrete wavelet transform is traditionally used to decompose BP into additive components. The first discrete wavelet transform was invented by the Hungarian mathematician Alfred Haar (1910-1920). In parallel with this method, in the 70s and 80s, the idea of a time series analysis method called SSA (Singular Spectrum Analysis) arose in Russia, the method was called "Caterpillar". During the existence of the method, it has received an extension of its application – automation of the allocation of trend and cyclic components of BP has been developed. Using the example of a study of the real time series of TRAFFAT, two methods of decomposition time series into additive components are considered. The complexity of determining the initial parameters is compared, the applicability to the decomposition of real time series is tested, and the quality of decomposition by both methods of one reference time series is compared. An assessment of the quality of the decomposition of the time series into components was made, as well as a comparison of the two methods in terms of the complexity of the analyst's application and the possibility of automating the selection of parameters.