MIMO (multiple-input multiple-output) radar provides much more flexibility than the traditional radar for its ability to realize far more observation channels than the actual number of T/R (transmit and receive) elements. Designing the array of MIMO imaging radar, the commonly used virtual array theory generally assumes that all elements are placed on the same line. However, due to the physical size of the antennas and coupling effect between T/R elements, a certain height difference between T/R arrays is essential, resulting in the defocusing of edge points of the scene. On the other hand, the virtual array theory implies far-field approximation, leading to inevitable high grating lobes in the imaging result of near-field edge points of the scene observed by common MIMO array. To tackle these problems, this paper derives the relationship between target’s PSF (point spread function) and pattern of T/R arrays, by which the design criterion of near-field imaging MIMO array is presented. Firstly, the proper height between T/R arrays is designed to focus the near-field edge points well. Secondly, the far-field array is modified to suppress the grating lobes in the near-field area. Finally, the validity of the proposed methods is verified by simulations and an experiment.

In this paper, we study the asymptotic behavior of the sequential empirical process and the sequential empirical copula process, both constructed from residuals of multivariate stochastic volatility models. Applications for the detection of structural changes and specification tests of the distribution of innovations are discussed. It is also shown that if the stochastic volatility matrices are diagonal, which is the case if the univariate time series are estimated separately instead of being jointly estimated, then the empirical copula process behaves as if the innovations were observed; a remarkable property. As a by-product, one also obtains the asymptotic behavior of rank-based measures of dependence applied to residuals of these time series models.

When dealing with limited sample sizes or missing values in time series data, achieving high accuracy in forecasting becomes challenging. This challenge is particularly common in wind energy forecasting, where many wind farms lack complete data. In this paper, we employ the widely-used ARIMA (Autoregressive Integrated Moving Average) model for time series forecasting. To address the difficulties posed by limited sample sizes and missing values, we adopt a unique approach by utilizing multiple ARIMA models for different datasets. A key distinction from other multiple models methods for time series forecasting lies in each model within our approach using its own dataset, making the fusion process more intricate. To overcome this, we incorporate neural networks and two techniques for model fusion: direct fusion with a learning mechanism and compensation for missing data through training. For each ARIMA model, we introduce a noise estimation method to circumvent the white noise assumptions inherent in ARIMA models. Finally, we apply these methods to wind energy prediction, and our experimental results showcase a significant enhancement in forecasting accuracy.

Leishmaniasis is the third most common vector-borne disease and a very important protozoan infection. Cutaneous leishmaniasis is one of the most common types of leishmaniasis infectious diseases with up to 2 million occurrences of new cases each year worldwide. A dynamic transmission multivariate time series model was applied to the data to account for overdispersion and evaluate the effects of three environmental layers as well as seasonality in the data. Furthermore, ecological niche modeling was used to investigate the geographical suitable conditions for cutaneous leishmaniasis using temperature, precipitation and altitude as environmental layers, together with the leishmaniasis presence data. A retrospective analysis of the cutaneous leishmaniasis spatial data in Afghanistan between 2003 and 2009 indicates a steady increase from 2003 to 2007, a small decrease in 2008, then another increase in 2009. An upward trend and regularly repeating patterns of highs and lows was observed related to the months of the year which suggests seasonality effect in the data. Two peaks were observed in the disease occurrence-- January to March and September to December -- which coincide with the cold period. Ecological niche modelling indicates that precipitation has the greatest contribution to the potential distribution of leishmaniasis.

The relaxation process of lithium batteries caused by load variation is considered. It is shown that such processes have strong dependence on internal physical and chemical processes and battery technical conditions. Theoretical expressions of the relaxation process caused by a step-like load variation have been obtained for 1^st and 2^nd order equivalent electrical circuits. The experimental investigations show that the obtained models fit the real relaxation processes and the behavior of the identified parameters could be explained by specific features of physical and chemical processes within the lithium battery. It should be noted that the obtained results can be generalized for a different type of electrochemical power source. The proposed approach makes it possible to provide means for electrochemical power source characterization and diagnostic, the main advantages of which are good time localization of measurement procedures and inexpensive apparatus implementation.

The anomaly detection task is very important in computer science. And there are a lot of anomaly detection methods. Different from some thresholding methods, some unsupervised methods could make us get more accurate and faster result, which is the object of the project. In this paper, I tried to use EWMA and some other methods in two datasets: Webank time consuming indicators dataset and AIOps Challenge dataset. The paper consists nine parts: background of the project, related work, description of algorithms, implementation details, experimental setup and data sets used, experimental results and discussion, future directions, reference and meeting notes.

The aim of this study is to analyze the characteristics of drought such as intensity, cumulative curves and trends, based on SPEI (Standardized Precipitation Evapotranspiration Index) at 8 stations in Korea from 1981 to 2010. The traditional SPEI is based on Thornthwaite equation for estimating evapotranspiration; SPEI_th. However, a standard of agricultural water management in Korea suggests FAO Penman-Monteith equation; SPEI_pm. In this study, we analyzed the intensity and trends of drought using SPEI_th and SPEI_pm, respectively, and analyzed the relationship between them. Both of central and southern region, the SPEIs were below -1.0 (moderated drought) for the periods May-August in the representative drought year such as 1988, 2001, and 2008-09. The frequency of drought was higher in southern region than central region. In addition, SPEI_pm showed slightly more intensive drought rather than SPEI_th except for Chuncheon and Gwangju. In 5 stations except for Cheoncheon, Gwangju and Jinju, the cumulative probability that SPEI_pm is below -1.5 was significantly increased from 1981-1995 to 1996-2010. As the results of drought trends, the increasing trend of SPEIs was shown on fall season, and the cumulative probability that SPEI_pm is below -1.5 was also significantly increased.

We study the problem of predicting time series data using the autoregressive integrated moving average (ARIMA) model in an online manner. Existing algorithms require model selection, which is time consuming and inapt for the setting of online learning. Using adaptive online learning techniques, we develop algorithms for fitting ARIMA models with fewest possible hyperparameters. We analyse the regret bound of the proposed algorithms and examine their performance using experiments on both synthetic and real world datasets

Time irreversibility, i.e. the lack of invariance of the statistical properties of a system under time reversal, is a fundamental property of all systems operating out of equilibrium. Time reversal symmetry is associated with important statistical and physical properties and is related to the predictability of the system generating the time series. Over the past fifteen years, various methods to quantify time irreversibility in time series have been proposed, but these can be computationally expensive. Here we propose a new method, based on permutation entropy, which is essentially parameter-free, temporally local, yields straightforward statistical tests, and has fast convergence properties. We apply this method to the study of financial time series, showing that stocks and indices present a rich irreversibility dynamics. We illustrate the comparative methodological advantages of our method with respect to a recently proposed method based on visibility graphs, and discuss the implications of our results for financial data analysis and interpretation.

Due to the long duration and high cost of traditional pumping tests, the response of well water level to seismic wave, earth tide, and barometric pressure provides a feasible method for determining continuous changes in aquifer hydraulic parameters. Aiming at the problem that the response phase shift of well BB water level to tidal tide M2 is greater than that of tide O1, this paper preferentially calculated the time series changes of S, Be, n and BKu based on the response mechanism of well water level to barometric pressure and earth tide and with the help of smooth moving method. Then by using the mixed flow model, the variation of transmissivity and leakage coefficient over time were simultaneously obtained, and the evolution process and characteristics of aquifer parameters near well BB caused by the Wenchuan earthquake were ultimately discussed. The calculation results are basically consistent with the previous pumping test, and have been verified and compared by using other scholars' methods. This solving process avoids the problems such as excessive dependence on initial values, multiple solutions, and unstable tide O1, which has a promoting effect on the study of the impact of seismic activity on aquifer systems.

This study aims to spatially analyze the distribution characteristics of vacant homes in Asan-si, Chungcheongnam-do, and understand the differences in factors causing vacant homes by type. We use a variety of statistical methods to examine these factors and identify key influencing factors such as the number of vacant stores, changes in overall population, land use complexity, and physical characteristics of land and buildings. The findings reveal that the factors contributing to the occurrence of vacant homes vary significantly by region and property type, highlighting the need for region-specific policies. For instance, in old town areas, small lot ratios and land use complexity are significant, while in rural village, the average number of floors and land use complexity play a major role. This study underscores the diversity of factors influencing vacant homes, suggesting that policies should be tailored to the unique characteristics of different regions to effectively address this issue.

While increasing empirical evidence suggests that global time series forecasting models can achieve better forecasting performance than local ones, there is a research void regarding when and why the global models fail to provide a good forecast. This paper uses anomaly detection algorithms and Explainable Artificial Intelligence (XAI) to answer when and why a forecast should not be trusted. To address this issue, a dashboard was built to inform the user regarding (i) the relevance of the features for that particular forecast, (ii) which training samples most likely influenced the forecast outcome, (iii) why the forecast is considered an outlier, and (iv) provide a range of counterfactual examples to understand value changes, in the feature vector or the predicted value, can lead to a different outcome. Moreover, a modular architecture and a methodology were developed to iteratively remove noisy data instances from the train set, to enhance the overall global time series forecasting model performance. Finally, to test the effectiveness of the proposed approach, it was validated on two publicly available real-world datasets.

The understanding of water quality and its underlying processes is important for the protection of aquatic environments enabling the rare opportunity of access to a domain expert. Hence, an explainable AI (XAI) framework is proposed that is applicable to multivariate time series resulting in explanations that are interpretable by a domain expert. The XAI combines in three steps a data-driven choice of a distance measure with explainable cluster analysis through supervised decision trees. The multivariate time series consists of water quality measurements, including nitrate, electrical conductivity, and twelve other environmental parameters. The relationships between water quality and the environmental parameters are investigated by identifying similar days within a cluster and dissimilar days between clusters. The XAI does not depend on prior knowledge about data structure, and its explanations are tendentially contrastive. The relationships in the data can be visualized by a topographic map representing high-dimensional structures. Two comparable decision-based XAIs were unable to provide meaningful and relevant explanations from the multivariate time series data. Open-source code in R for the three steps of the XAI framework is provided.

Real-world time series data sets contain a combination of linear and nonlinear patterns, making the time series forecasting problem more challenging. In this paper, a new hybrid methodology is introduced for forecasting univariate time series data sets using a multiplicative error modeling approach. An autoregressive integrated moving average (ARIMA) model is combined with an autoregressive neural network (ARNN) for improving the predictions of individual forecast models. The proposed multiplicative ARIMA-ARNN model glorifies the chances of capturing the different combinations of linear and nonlinear patterns in time series. The model shows outstanding performance on six standard time-series data sets compared to other widely used single and hybrid forecasting models.

In this paper, we study the usage of machine learning models for sales time series forecasting. The effect of machine learning generalization has been considered. A stacking approach for building regression ensemble of single models has been studied. The results show that using stacking technics, we can improve the performance of predictive models for sales time series forecasting.

We define a new seasonal forecasting method based on fuzzy transforms. We use the best interpolating polynomial for extracting the trend of the time series and generate the inverse fuzzy transform on each seasonal subset of the universe of discourse for predicting the value of a an assigned output. Like first example, we use the daily weather dataset of the municipality of Naples (Italy) starting from data collected from 2003 till to 2015 making predictions on the following outputs: mean temperature, max temperature and min temperature, all considered daily. Like second example, we use the daily mean temperature measured at the weather station “Chiavari Caperana” in the Liguria Italian Region. We compare the results with our method, the average seasonal variation, ARIMA and the usual fuzzy transforms concluding that the best results are obtained under our approach in both examples.

Time series forecasting has been a challenging area in the field of Artificial Intel-ligence. Various approaches such as linear Neural Networks, Recurrent Linear Neural Networks, Convolutional Neural Networks and recently Transformers have been attempted for the time series forecasting domain. Although, Trans-former-based architectures have been outstanding in the Natural Language Pro-cessing domain, especially in autoregressive language modeling, the initial at-tempts to use transformers in the time series arena have met with mixed success. One of the recent papers demonstrated that modeling the multi-variate time se-ries problem as independent channels on a transformer architecture produced lower mean square and mean absolute errors on benchmarks, however, another recent paper claimed that a simple linear neural network out-performs previous approaches including transformer-based designs. We investigate this paradox in detail comparing the linear Neural Network and Transformer based designs, provide insights to why a certain approach may be better for a particular type of problem. We also improve upon the recently proposed simple linear Neural Network based architecture by using dual pipelines with batch normalization and reversible instance normalization. Our enhanced architecture outperforms all existing architectures for time series forecasting on majority of the popular benchmarks.

Due to increase demand of food grain in the world, assessment of yield before actual production is important in making policies and decisions in agricultural production system. For a large area, forecast models developed from vegetation indices derived from remote sensing satellite data possesses the potential to give quantitative and timely information on crops over large areas. Different vegetation indices are being made used for this purpose, however, their efficiency in estimating crop yield is needed to be certainly tested. In this study, wheat yield forecast was derived by regressing ground truthing yield data against time series of spatial vegetation indices for the 2013 to 2019 growing seasons. These spatial vegetation indices derived from Landsat 8 image data: Normalized Difference Vegetation Index (NDVI) and Soil Adjusted Vegetation Index (SAVI) were compared to evaluate the most appropriate index that performs better in forecasting wheat production at Karcag, Kunhegyes and Ecsegfalva settlements in Jász-Nagykun-Szolnok county, in the Northern Great Plain region of central Hungary. The best time for making wheat yield prediction with Landsat 8- SAVI and NDVI was found to be the beginning of ripening period (160th day of the year) with higher correlation between the vegetation indices and the wheat yield. The validation results revealed that the model from SAVI provides more consistent and accurate forecasts yield compared to NDVI. The SAVI model forecast yield for the validation years, 2018 and 2019 were within 6.00% and 4.41% of the final reported values while that of NDVI model were within 8.31% and 6.27%. Nash-Sutcliffe efficiency index is positive with E1= 0.99 for the model from SAVI and for NDVI, E1=0.57, which connote that the forecasting method developed and evaluated performs acceptable forecast efficiency.

Noise model selection criteria has a significant impact on identifying the stochastic noise proper-ties of any GNSS daily coordinate time series. The low-frequency random walk noise existing in these time series could lead to overestimation of the tectonic rate, so it is of great significance to accurately detect the random walk component. This study focuses on noise model estimation cri-terion (BIC_tp) derived from the AIC and the BIC by introducing 2π factors. It is more sensitive to abnormal steps (random jumps). Using observation data from 72 GNSS stations from 1992 to 2022 and simulated data, four combined noise models are used to explore the impacts of time se-ries lengths (ranging from2 to 24 years) and data loss (between 2% and 30%) on noise models and velocity estimation. The results show that as the time length increased, the selected optimal noise model, and the estimated uncertainty of the tectonic trend with different data gap, gradually con-verge. When the time length is short (less than 8 years), it could lead to the FNRWWN, FNWN, and PLWN models being mistakenly estimated as GGMWN models, thereby affecting the accura-cy of determining the station velocity parameters. When the time length is 12 years, the RW noise component is more probably detected, As the time length increases, the impact of RW on velocity uncertainty is weakened. Finally, we conclude that for a time series with a minimum time length of 12 years, both the selection of the optimal stochastic noise model and the estimation of the ve-locity parameters are reliable.

The goal of clustering is to identify common structures in a data set by forming groups of homogeneous objects. The observed characteristics of many economic time series motivated the development of classes of distributions that can accommodate properties such as heavy tails and skewness. Thanks to its flexibility, the Skewed Exponential Power Distribution (also called Skewed Generalized Error Distribution) ensures a unified and general framework for clustering possibly skewed and heavy tailed time series. This paper develops a clustering procedure of model-based type, assuming that the time series are generated by the same underlying probability distribution but with different parameters. Moreover, we propose to optimally combine the estimated parameters to form the clusters with an entropy weighing $k$-means approach. The usefulness of the proposal is showed by means of application to financial time series, demonstrating also how the obtained clusters can be used to form portfolio of stocks.

The removal of non-climatic biases, so-called inhomogeneities, from long climatic records needs sophistically developed statistical methods. One principle is that usually the differences between a candidate series and its neighbour series are analysed instead of directly the candidate series, in order to neutralize the possible impacts of regionally common natural climate variation on the detection of inhomogeneities. In most homogenization methods, two main kinds of time series comparisons are applied, i.e. composite reference series or pairwise comparisons. In composite reference series the inhomogeneities of neighbour series are attenuated by averaging the individual series, and the accuracy of homogenization can be improved by the iterative improvement of composite reference series. By contrast, pairwise comparisons have the advantage that coincidental inhomogeneities affecting several station series in a similar way can be identified with higher certainty than with composite reference series. In addition, homogenization with pairwise comparisons tends to facilitate the most accurate regional trend estimations. A new time series comparison method is presented here, which combines the use of pairwise comparisons and composite reference series in a way that their advantages are unified. This time series comparison method is embedded into the ACMANT homogenization method, and tested in large, commonly available monthly temperature test datasets.

This work focuses on analyzing acoustic emission (AE) signals as a means to predict failure in structures. Two main approaches are considered: (i) long-range correlation analysis using both the Hurst (H) and the Detrended Fluctuation Analysis (DFA) exponents, and (ii) natural time domain (NT) analysis. These methodologies are applied to the data collected from two application examples: a glass fiber reinforced polymeric plate and a spaghetti bridge model, where both structures were subjected to increasing loads until collapse. A traditional (AE) signal analysis is also performed to reference the study of the other methods. Results indicate that the proposed methods yield a reliable indication of failure in the studied structures.

The aerospace industry develops prognosis and health management algorithms to ensure better safety on board. Particularly for in-flight controls where jamming is dreaded. For that, vibration signals are monitored to predict future defect occurrences. However, time series are not labeled according to severity level, and the user can only assess the system health from the data mining procedure. To that extent, we developed a clustering algorithm using a deep neural network core. We encoded the time series into pictures to be feed into an artificially trained neural network: U-NET. From the segmented output, one-dimensional information on cluster frontiers is extracted and filtered without any parameter selection. Then, a kernel density estimation finally transforms the signal into an empirical density. Ultimately, a Gaussian mixture model extracts the latter independent components. The method empowered us to reveal different degrees of severity faults in the studied data, with their respective likelihood without prior knowledge. We compared it to state-of-the-art machine learning algorithms. However, internal clustering results evaluation for time series is an open question. As state-of-the-art indexes were not producing relevant results, we built a new indicator to fulfill this task. We applied the whole method to an actuator consisting of an induction machine linked to a ball screw. This study lays the groundwork for future training of diagnosis and prognosis structures in the health management framework.

Measuring bias is important as it helps identify flaws in quantitative forecasting methods or judgmental forecasts. It can, therefore, potentially help improve forecasts. Despite this, bias tends to be under-represented in the literature: many studies focus solely on measuring accuracy. Methods for assessing bias in single series are relatively well-known and well-researched, but for datasets containing thousands of observations for multiple series, the methodology for measuring and reporting bias is less obvious. We compare alternative approaches against a number of criteria when rolling-origin point forecasts are available for different forecasting methods and for multiple horizons over multiple series. We focus on relatively simple, yet interpretable and easy-to-implement metrics and visualization tools that are likely to be applicable in practice. To study the statistical properties of alternative measures we use theoretical concepts and simulation experiments based on artificial data with predetermined features. We describe the difference between mean and median bias, describe the connection between metrics for accuracy and bias, provide suitable bias measures depending on the loss function used to optimise forecasts, and suggest which measures for accuracy should be used to accompany bias indicators. We propose several new measures and provide our recommendations on how to evaluate forecast bias across multiple series.

In this study, we present a novel approach to estimate the Hurst exponent of time series data using a variety of machine learning algorithms. The Hurst exponent is a crucial parameter in characterizing long-range dependence in time series, and traditional methods such as Rescaled Range (R/S) analysis and Detrended Fluctuation Analysis (DFA) have been widely used for its estimation. However, these methods have certain limitations, which we sought to address by modifying the R/S approach to distinguish between fractional Lévy and fractional Brownian motion, and by demonstrating the inadequacy of DFA and similar methods for data that resembles fractional Lévy motion. This inspired us to utilize machine learning techniques to improve the estimation process. In an unprecedented step, we train various machine learning models, including LightGBM, MLP, and AdaBoost, on synthetic data generated from random walks, namely fractional Brownian motion and fractional Lévy motion, where the ground truth Hurst exponent is known. Meaning that we can initialize and create these stochastic processes with a scaling Hurst/scaling exponent which, is then used as the ground truth for training. Furthermore, we perform the continuous estimation of the scaling exponent directly from the time series, without resorting to the calculation of the power spectrum or other sophisticated preprocessing steps, as done in past approaches. Our experiments reveal that the machine learning-based estimators outperform traditional R/S analysis and DFA methods in estimating the Hurst exponent, particularly for data akin to fractional Lévy motion. Validating our approach on real-world financial data, we observe a divergence between the estimated Hurst/scaling exponents and results reported in the literature. Nevertheless, the confirmation provided by known ground truths reinforces the superiority of our approach in terms of accuracy. This work highlights the potential of machine learning algorithms for accurately estimating the Hurst exponent, paving new paths for time series analysis. By marrying traditional finance methods with the capabilities of machine learning, our study provides a novel contribution towards the future of time series data analysis.

Machine learning methods have widely been applied to detect anomalies in machine and cutting tool behavior during lathe or milling. However, detecting anomalies in the workpiece itself did not get the same attention by researchers. That is why in this article, the authors present a pub-licly available multivariate time series dataset which was recorded during milling of 16MnCr5. Due to artificially introduced, though realistic anomalies in the workpiece the dataset can be ap-plied for anomaly detection. By using a convolutional autoencoder as a first model good results in detecting the location of the anomalies in the workpiece were achieved. Furthermore, milling tools with two different diameters where used which led to a dataset eligible for transfer learn-ing. The objective of this article is to provide researchers with a real-world time series dataset of the milling process which is suitable for modern machine learning research topics like anomaly detection and transfer learning.

Time series data are significant and are derived from temporal data, which involve real numbers representing values collected regularly over time. Time series have a great impact on many types of data. However, time series have anomalies. We introduce hybrid algorithm named novel matrix profile (NMP) to solve the all-pairs similarity search problem for time series data. The proposed NMP inherits the features from two state-of-the art algorithms: similarity time-series automatic multivariate prediction (STAMP), and short text online microblogging protocol (STOMP). The proposed algorithm caches the output in an easy-to-access fashion for single- and multidimensional data. The proposed NMP algorithm can be used on large data sets and generates approximate solutions of high quality in a reasonable time. The proposed NMP can also handle several data mining tasks. It is implemented on a Python platform. To determine its effectiveness, it is compared with the state-of-the-art matrix profile algorithms i.e., STAMP and STOMP. The results confirm that the proposed NMP provides higher accuracy than the compared algorithms.

Traditional applications of Interferometric Synthetic Aperture Radar (InSAR) data involved inverting an interferogram stack to determine the average displacement velocity. While this approach has useful applications in continuously deforming regions, much information is lost by simply fitting a line through the time series. Thanks to regular acquisitions across most of the the world by the ESA Sentinel-1 satellite constellation, we are now in a position to explore opportunities for near-real time deformation monitoring. In this paper we present a simple statistical approach for detecting offsets and gradient changes in InSAR time series. Our key assumption is that 5 years of Sentinel-1 data is sufficient to calculate the population standard deviation of the detection variables. Our offset detector identifies statistically significant peaks in the first, second and third difference series. The gradient change detector identifies statistically significant movements in the second derivative series. We exploit the high spatial resolution of Sentinel-1 data and the spatial continuity of geophysical deformation signals to filter out false positive detections that arise due to signal noise. When combined with near-real time processing of InSAR data these detectors, particularly the gradient change, could be used to detect incipient ground deformation associated with geophysical phenomena, for example from landslides or volcanic eruptions.

Modern energy systems collect high volumes of data that can provide valuable information about energy consumption. Electric companies can now use historical data to make informed decisions on energy production by forecasting the expected demand. Many deep learning models have been proposed to deal with these type of time series forecasting problems. Deep neural networks, such as recurrent or convolutional, can automatically capture complex patterns in time series data and provide accurate predictions. In particular, Temporal Convolutional Networks (TCN) are a specialised architecture that has advantages over recurrent networks for forecasting tasks. TCNs are able to extract long-term patterns using dilated causal convolutions and residual blocks, and can also be more efficient in terms of computation time. In this work, we propose a TCN-based deep learning model to improve the predictive performance in energy demand forecasting. Two energy-related time series with data from Spain have been studied: the national electric demand, and the power demand at charging stations for electric vehicles. An extensive experimental study has been conducted, involving more than 1900 models with different architectures and parametrisations. The TCN proposal outperforms the forecasting accuracy of Long Short-Term Memory (LSTM) recurrent networks, which are considered the state-of-the-art in the field.

The study of order patterns of three equally spaced values $x_t,x_{t+d},x_{t+2d}$ in a time series is a powerful tool. The lag $d$ is changed in a wide range so that differences of frequencies of order patterns become autocorrelation functions. Similar to a spectrogram in speech analysis, four ordinal autocorrelation functions are used to visualize big data series, as for instance heart and brain activity over many hours. The method applies to real data without preprocessing, outliers and missing data do not matter. On the theoretical side, we study properties of order correlation functions and show that the four autocorrelation functions are orthogonal in a certain sense. An analysis of variance of a modified permutation entropy can be performed with four variance components associated with the functions.

This paper has three objectives, the first is to present a detailed overview in the form of a tutorial for the developments of several key quantile time series modelling approaches. The second objective is to develop a general framework to represent such quantile models in a unifying manner in order to easily develop extensions and connections between existing models that can then be developed to further extend these models in practice. In this regard, the core theme of the paper is to provide perspectives to a general audience of core components that go into construction of a quantile time series model and then to explore each of these core components in detail. The paper is not addressing the concerns of estimation of these models, as there is existing literature on these aspects in many settings, we provide references to relevant works on these aspects in several classes of model. Instead, the focus is rather to provide a unified framework to construct such models for practitioners, therefore the focus is instead on the properties of the models and links between such models from a constructive perspective. The third objective is to compare and discuss the application of the different quantile time series models on several sets of interesting demographic and mortality based time series data sets of relevance to life insurance analysis. The exploration included detailed mortality, fertility, births and morbidity data in several countries with more detailed analysis of regional data in England, Wales and Scotland.

Accurate streamflow forecasting is crucial for effectively managing water resources, particularly in countries like Colombia, where hydroelectric power generation significantly contributes to the national energy grid. Although highly interpretable, traditional deterministic, physically-driven models often suffer from complexity and require extensive parameterization. Data-driven models like Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) networks offer simplicity and performance but cannot quantify uncertainty. This work introduces Sparse Variational Gaussian Processes (SVGPs) for forecasting streamflow contributions. The proposed SVGP model reduces computational complexity compared to traditional Gaussian Processes, making it highly scalable for large datasets. The methodology employs optimal hyperparameters and shared inducing points to capture short-term and long-term relationships among reservoirs. Training, validation, and analysis of the proposed approach consider the streamflow dataset from 23 geographically dispersed reservoirs recorded during twelve years in Colombia. Performance assessment reveals that the proposal outperforms baseline Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) models in three key aspects: adaptability to changing dynamics, provision of informative confidence intervals through Bayesian inference, and enhanced forecasting accuracy. Therefore, the SVGP-based forecasting methodology offers a scalable and interpretable solution for multi-output streamflow forecasting, thereby contributing to more effective water resource management and hydroelectric planning.

Multivariate Time Series Classification (MTSC) is one of most important tasks in time series analysis, aiding in activities such as human motion recognition and medical diagnostics. Existing methods for MTSC do not explicitly model temporal differences and generalize the idea of temporal difference into a efficient temporal module. Additionally, existing methods are not yet able to capture cross-variable relationships well during network training. As a result, they are unable to achieve convincing feature representation, leading to suboptimal classification accuracy. In this paper, we propose a novel MTSC model called Temporal Difference and Cross-variate Fusion Network (TDCFN), which integrates a two-stream differential LSTM network and a cross-variate feature extraction network to enhance feature representation. TDCFN achieves superior classification accuracy by capturing dynamic temporal evolution and inter-variable relationships. The experimental results show that TDCFN can achieve competitive performance with state-of-the-art multivariate time series classification approaches.

Early detection of wildfires has been limited using the sun-synchronous orbit satellites due to their low temporal resolution and wildfires’ fast spread in the early stage. NOAA’s geostationary weather satellites GOES-R can acquire images every 15 minutes at 2km spatial resolution, and have been used for early fire detection. However, advanced processing algorithms are needed to provide timely and reliable detection of wildfires. In this research, a deep learning framework, based on Gated Recurrent Units (GRU), is proposed to detect wildfires at early stage using GOES-R dense time series data. GRU model maintains good performance on temporal modelling while keep a simple architecture, makes it suitable to efficiently process time-series data. 36 different wildfires in North and South America under the coverage of GOES-R satellites are selected to assess the effectiveness of the GRU method. The detection times based on GOES-R are compared with VIIRS active fire products at 375m resolution in NASA’s Fire Information for Resource Management System (FIRMS). The results show that GRU-based GOES-R detections of the wildfires are earlier than that of the VIIRS active fire products in most of the study areas. Also, results from proposed method offer more precise location on the active fire at early stage than GOES-R Active Fire Product in mid-latitude and low-latitude regions.

The evaluation of geometric defects is necessary in order to maintain the integrity of structures over time. These assessments are designed to detect damages of structures and ideally help inspectors to estimate the remaining life of structures. Current methodologies for monitoring structural systems, while providing useful information about the current state of a structure, are limited in the monitoring of defects over time and in linking them to predictive simulation. This paper presents a new approach to the predictive modeling of geometric defects. A combination of segmented from point clouds are parametrized using the convex hull algorithm to extract features from detected defects, and a stochastic dynamic model is then adapted to these features to model the evolution of the hull over time. Describing a defect in terms of its parameterized hull enables consistent temporal tracking for predictive purposes, while implicitly reducing data dimensionality and complexity as well. In this study, 2D point clouds analogous to information derived from point clouds were first generated over simulated life-cycles. The evolutions of point cloud hull parameterizations were modeled as stochastic dynamical processes via autoregressive integrated moving average (ARIMA) and vectorized autoregression (VAR) and compared against ground truth. The results indicate that this convex hull approach provides consistent and accurate representations of defect evolution across a range of defect topologies and is reasonably robust to noisy measurements, however assumptions regarding the underlying dynamical process play a significant the role in predictive accuracy. The results were then validated on experimental data from fatigue testing with high accuracy. Longer term, the results of this work will support finite element model updating for predictive analysis of structural capacity.

GNSS time series prediction plays a significant role in monitoring crustal plate motion, landslide detection, and maintenance of the global coordinate framework. Long Short-Term Memory (LSTM), a deep learning model has been widely applied in the field of high-precision time series prediction especially when combined with Variational Mode Decomposition (VMD) to form the VMD-LSTM hybrid model. To further improve the prediction accuracy of the VMD-LSTM model, this paper proposes a dual variational modal decomposition long short-term memory (DVMD-LSTM) model to effectively handle the noise in GNSS time series prediction. This model extracts fluctuation features from the residual terms obtained after VMD decomposition to reduce the prediction errors associated with residual terms in the VMD-LSTM model. Daily E, N, and U coordinate data recorded at multiple GNSS stations between 2000 and 2022 are used to validate the performance of the proposed DVMD-LSTM model. The experimental results demonstrate that compared to the VMD-LSTM model, the DVMD-LSTM model achieves significant improvements in prediction performance across all measurement stations. The average RMSE is reduced by 9.86%, and the average MAE is reduced by 9.44%. Furthermore, the average accuracy of the optimal noise model for the predicted results is improved by 36.50%, and the average speed accuracy of the predicted results is enhanced by 33.02%. These findings collectively attest to the superior predictive capabilities of the DVMD-LSTM model, thereby enhancing the reliability of the predicted results.

Non-neural Machine Learning (ML) and Deep Learning (DL) are used to predict system failures in industrial maintenance. However, only a few studies have assessed the effect of varying the amount of past data used to make a prediction and the extension in the future of the forecast. This study evaluates the impact of the size of the reading window and of the prediction window on the performances of models trained to forecast failures in three data sets of (1) an industrial wrapping machine working in discrete sessions, (2) an industrial blood refrigerator working continuously and (3) a nitrogen generator working continuously. A binary classification task assigns the positive label to the prediction window based on the probability of a failure to occur in such an interval. Six algorithms (logistic regression, random forest, support vector machine, LSTM, ConvLSTM and Transformers) are compared using multivariate time series. The dimension of the prediction windows plays a crucial role and the results highlight the effectiveness of DL approaches in classifying data with diverse time-dependent patterns preceding a failure and the effectiveness of ML approaches in classifying similar and repetitive patterns preceding a failure.

Augmented reality (AR) provides an opportunity for mobile fitness applications to show users real-time feedback on their current fitness activity. For such applications, it is essential to accurately track the user’s current fitness activity using available mobile sensors, such as inertial measurement units (IMUs). Convolutional neural networks (CNNs) have been shown to produce strong results in different time series classification tasks, including the recognition of activities of daily living. However, fitness activities can present unique challenges to the human activity recognition task (HAR), including greater similarity between individual activities and fewer available data for model training. In this paper, we evaluate the applicability of CNNs to the fitness activity recognition task (FAR) using IMU data and determine the impact of input data size and sensor count on performance. For this purpose, we adapted three existing CNN architectures to the FAR task and designed a fourth CNN variant, which we call the scaling fully convolutional network (Scaling-FCN). We designed a preprocessing pipeline and recorded a running exercise data set with 20 participants, in which we evaluated the respective recognition performances of the four networks, comparing them with three traditional machine learning methods commonly used in HAR. On our data set, all CNN architectures significantly outperformed traditional machine learning methods, reaching up to 97.14±1.36% classification accuracy on the test set for ResNet. Whereas a reduced input data size invariably led to a performance loss, removing specific sensors improved the performance of all CNN architectures, with our Scaling-FCN reaching the highest accuracy of 99.86±0.11%. Our results suggest that CNNs are generally well suited for fitness activity recognition, and noticeable performance improvements can be achieved if sensors are dropped selectively.

With an explosion of data in the nearly every domain, from physical and environmental sciences to econometrics and even social science, we have entered a golden era of time-domain data science. In addition to ever increasing data volumes and varieties of time-series, there's a plethora of techniques available to analyses them. Unsurprisingly, machine learning approaches are very popular. In environmental sciences (ranging from climate studies to space weather/solar physics), machine learning (ML )and deep learning (DL) approaches complement the traditional data assimilation approaches. In solar and astrophysics, multiwavelength time-series or lightcurves along with observations of other messengers like gravitational waves provide a treasure trove of time-domain data for ML/DL approaches for modeling and forecasting. In this regard, deep learning algorithms such as recurrent neural networks (RNNs) should prove extremely powerful for forecasting as it has in several other domains. Such methods agnostic of the physics can only predict transient flares that are represented in the original distribution trained on (eg. coloured noise fluctuations) and not special, isolated episodes (eg. a one-off outburst like a major coronal mass ejection) potentially distinguishing them. Therefore it is vital to test robustness of these techniques ; here we attempt to make a small contribution to this by exploring sensitivity of RNNs with some rudimentary experiments. We test the performance of a very successful class of RNNs, the Long Short Term Memory (LSTM) algorithms with simulated lightcurves. As an example, we focus on univariate forecasting of time-series (or lightcurves) characteristic certain variable astrophysical objects (eg. active galactic nuclei or AGN). Specifically, we explore the sensitivity of training and test losses to key parameters of the LSTM network and data characteristics namely gaps and complexity measured in terms of number of Fourier components. We find that typically, the performances of LSTMs are better for pink or flicker noise type sources. The key parameters on which performance is dependent are batch size for LSTM and the gap percentage of the lightcurves. While a batch size of $10-30$ seems optimal, the most optimal test and train losses are under $10 \%$ of missing data for both periodic and random gaps in pink noise. The performance is far worse for red noise. This compromises detectability of transients. Thus, we show that generative models (time-series simulations) are excellent guides for use of RNN-LSTMs in building forecasting systems

The environmental issues we are currently facing require long-term prospective efforts for sustainable growth. Renewable energy sources seem to be one of the most practical and efficient alternatives in this regard. Understanding a nation's pattern of energy use and renewable energy production is crucial for developing strategic plans. No previous study has been performed to explore the dynamics of power consumption with the change in renewable energy production on a country-wide scale. In contrast, a number of deep learning algorithms demonstrated acceptable performance while handling sequential data in the era of data-driven predictions. In this study, we developed a scheme to investigate and predict total power consumption and renewable energy production time series for eleven years of data using a Recurrent Neural Network (RNN). The dynamics of the interaction between the total annual power consumption and renewable energy production are investigated through extensive Exploratory Data Analysis (EDA) and a feature engineering framework. The performance of the model is found satisfactory through the comparison of the predicted data with the observed data, visualization of the distribution of the errors and Root Mean Squared Error (RMSE) value of 0.084. Higher performance is achieved through the increase in the number of epochs and hyperparameter tuning. The proposed framework can be used and transferred to investigate the trend of renewable energy production and power consumption and predict the future scenarios for different communities. Incorporation of the cloud-based platform into the proposed pipeline may lead to real-time forecasting.

To detect aberrant human behaviors from large volume of passive data collected by smartphones in real time, we propose an online anomaly detection method using Hotelling’s T-squared test. The test statistic is a weighted average, with more weight on the between-individual component when there are little data available for the individual and more weight on the within-individual component when the data are adequate. The algorithm takes only O(1) run time in each update and the required memory usage is fixed after a pre-specified number of updates. The performance of the proposed method, in terms of accuracy, sensitivity and specificity, is consistently better than or equal to the offline method that it builds upon depending on the sample size of the individual data.

This article explores the required amount of time series points from a high-speed traffic network to accurately estimate the Hurst exponent. The methodology consists in designing an experiment using estimators that are applied to time series, followed by addressing the minimum amount of points required to obtain accurate estimates of the Hurst exponent in real-time. The methodology addresses the exhaustive analysis of the Hurst exponent considering bias behavior, standard deviation, mean square error, and convergence using fractional Gaussian noise signals with stationary increases. Our results show that the Whittle estimator successfully estimates the Hurst exponent in series with few points. Based on the results obtained, a minimum length for the time series is empirically proposed. Finally, to validate the results, the methodology is applied to real traffic captures in a high-speed network based on the IEEE 802.3ab standard.

In an epoch characterized by the swift pace of digitalization and urbanization, the essence of community well-being hinges on the efficacy of urban management. As cities burgeon and transform, the need for astute strategies to navigate the complexities of urban life becomes in-creasingly paramount. This study employs time series analysis to scrutinize citizen interactions with the coordinate-based problem mapping platform in the Municipality of Patras in Greece. The research explores the temporal dynamics of reported urban issues, with a specific focus on identifying recurring patterns through the lens of seasonality. The analysis, employing the sea-sonal decomposition technique, dissects time series data to expose trends in reported issues and areas of the city that might be obscured in raw big data. It accentuates a distinct seasonal pattern, with concentrations peaking during the summer months. The study extends its approach to forecasting, providing insights into the anticipated evolution of urban issues over time. Projec-tions for the coming years show a consistent upward trend in both overall city issues and those reported in specific areas, with distinct seasonal variations. This comprehensive exploration of time series analysis and seasonality provides valuable insights for city stakeholders, enabling informed decision-making and predictions regarding future urban challenges.

Background: Digital clinical measures collected via various digital sensing technologies such as smartphones, smartwatches, wearables, ingestible, and implantable are increasingly used by individuals and clinicians to capture health outcomes or behavioral and physiological characteristics of individuals. Time series classification (TSC) is very commonly used in modeling digital clinical measures. While deep learning models for TSC are very common and powerful, there exist some fundamental challenges. This review presents non-deep learning models commonly used for time series classification in biomedical applications that achieve high performance. Objective: We performed a systematic review to characterize the techniques used in time series classification of digital clinical measures throughout all stages of data processing and model building. Methods: We conducted a literature search on PubMed, and the Institute of Electrical and Electronics Engineers (IEEE), Web of Science, and SCOPUS databases using a range of search terms to retrieve peer-reviewed articles reporting academic research on digital clinical measures in the five year period between June 2016 and June 2021. We identified and categorized research studies based on the types of classification algorithms and sensor input types. Results: We found 452 papers in total from four different databases: PubMed, IEEE, Web of Science Database, and SCOPUS. After removing duplicates and irrelevant papers, 135 articles remained for detailed review and data extraction. Among these, engineered features using time series methods that were subsequently fed into widely-used machine learning classifiers was the most commonly used technique and also most frequently achieved the best performance metrics (77 out of 135 articles). Statistical modeling (24 out of 135 articles) algorithms were the second most common and also second best classification technique. Wavelet-based classification models (8 out of 135 articles) were also common. Electroencephalogram (29 out of 135 articles) was the most common data type used as an input. Accuracy was the most commonly reported performance metric, with 67.65% of articles reporting on accuracy. In this review paper, we provide summaries of signal pre-processing methods, feature engineering and selection methods, time series models, as well as model interpretations. Importantly, we found that about 50% of the papers only report one performance metric, which may result in a skewed view of overall performance. Conclusion: While high time series classification performance has been achieved in digital clinical, physiological, or biomedical measures, no standard benchmark datasets, modeling methods, or reporting methodology exist. There is no single widely used method for time series model development or feature interpretation– many different methods have proven successful.

InSAR and associated analytic methods can measure surface deformation from low earth orbit with a claimed accuracy of centimeters to millimeters. The realized accuracy depends on the area being measured and on the choice of analytic method, suggesting one choose a method in response to the area being measured. Here we consider a specific fixed analytic method and compare the results it produces to measurements gathered from other means in a variety of settings. In particular we compare Sentinel-1 InSAR with GPS at the Kilauea volcano around the 2018 eruption, with GPS in the city of Arica, Chile, and with public survey data at a decommissioned tailings mine. In addition, we compare two independent Sentinel-1 InSAR analyses for a railway station in Oslo, Norway. Our goal is estimate the accuracy of a fully automated Sentinel-1 InSAR pipeline in various settings. Our conclusions are that centimeter level accuracy is a reasonable claim in many, but not all settings, and that accuracy is typically not lost by using an automated pipeline, instead of hand-selecting and tuning parameters.

This paper realizes early bearing fault warning through bearing fault time series prediction, and proposes a bearing fault time series prediction model based on optimized maximum correlation kurtosis deconvolution (MCKD) and long short-term memory (LSTM) recurrent neural network to ensure bearings operation reliability. The model is based on lifecycle vibration signal of the bearing, to begin, the cuckoo search (CS) is utilized to optimize the parameter filter length L and deconvolution period T of MCKD, taking into account the influence and periodicity of the bearing time series, the fault impact component of the optimized MCKD deconvolution time series is improved. Then select the LSTM learning rate α depending on deconvolution time series. Finally, the dataset obtained through various preprocessing approaches are used to train and predict the LSTM model. The average prediction accuracy of the optimized MCKD-LSTM model is 26 percent higher than that of the original time series, proving the efficiency of this method, and the prediction results track the real fault data well, according to the XI'AN JIAOTONG University XJTU-SY bearing dataset.

Fractal behavior and long-range dependence are widely observed in measurements and characterization of traffic flow in high-speed computer networks of different technologies and coverage levels. This paper presents the results obtained when applying fractal analysis techniques on a time series obtained from traffic captures coming from an application server connected to the Internet through a high-speed link. The results obtained show that traffic flow in the dedicated high-speed network link have fractal behavior when the Hurst exponent is in the range of 0.5, 1, the fractal dimension between 1, 1.5, and the correlation coefficient between –0.5, 0. Based on these results, it is ideal to characterize both the singularities of the traffic and its impulsiveness during a fractal analysis of temporal scales. Finally, based on the results of the time series analyses, the fact that the traffic flows of current computer networks exhibit fractal behavior with a long-range dependency is reaffirmed.

One of the key components of application performance monitoring (APM) software is 2 AI/ML empowered data analytics for predictions, anomaly detection, event correlations and root 3 cause analysis. Time series metrics, logs and traces are three pillars of observability and the valuable 4 source of information for IT operations. Accurate, scalable and robust time series forecasting and 5 anomaly detection are desirable capabilities of the analytics. Approaches based on neural networks 6 (NN) and deep learning gain increasing popularity due to their flexibility and ability to tackle complex 7 non-linear problems. However, some of the disadvantages of NN-based models for distributed cloud 8 applications mitigate expectations and require specific approaches. We demonstrate how NN-models 9 pretrained on a global time series database can be applied to customer specific data using transfer 10 learning. In general, NN-models adequately operate only on stationary time series. Application 11 to non-stationary time series requires multilayer data processing including hypothesis testing for 12 data categorization, category specific transformations into stationary data, forecasting and backward 13 transformations. We present the mathematical background of this approach and discuss experimental 14 results from the productized implementation in Wavefront by VMware (an APM software) while 15 monitoring real customer cloud environments.

We present and benchmark FilterNet, a flexible deep learning architecture for time series classification tasks, such as activity recognition via multichannel sensor data. It adapts popular CNN and CNN-LSTM motifs which have excelled in activity recognition benchmarks, implementing them in a many-to-many architecture to markedly improve frame-by-frame accuracy, event segmentation accuracy, model size, and computational efficiency. We propose several model variants, evaluate them alongside other published models using the Opportunity benchmark dataset, demonstrate the effect of model ensembling and of altering key parameters, and quantify the quality of the models’ segmentation of discrete events. We also offer recommendations for use and suggest potential model extensions. FilterNet advances the state of the art in all measured accuracy and speed metrics on the benchmarked dataset, and it can be extensively customized for other applications.

Hand and arm gesture recognition using radio frequency (RF) sensing modality proves valuable in man-machine interface and smart environment. In this paper, we use time series analysis method for accurately measuring the similarity of the micro-Doppler (MD) signatures between the training and test data, thus providing improved gesture classification. We characterize the MD signatures by the maximum instantaneous Doppler frequencies depicted in the spectrograms. In particular, we apply the dynamic time warping (DTW) method and compare its performance with that of the long short-term memory (LSTM) network. Both methods take into account the values as well as the temporal evolution and trends of time series data. It is shown that the DTW method achieves high gesture classification rates and is robust to time misalignment.

Cost estimating based on building cost index plays an important role in project planning and management by providing accurate cost information. Recently, tremendous advances in cost estimating has been made but serious inaccuracies in it are still too frequently witnessed. This study aims to improve estimating accuracy for residential building costs in New Zealand. In this study, the New Zealand house prices index is involved in the transfer function models to produce forecasts of building costs for one-storey house, two-storey house, and town house in New Zealand. To demonstrate the effectiveness of the proposed models, this study compares the estimate results of the transfer function models with the univariate ARIMA models. The results indicate that the proposed transfer function models can achieve better outcomes than ARIMA models by considering the causality between building costs and New Zealand house prices. During the modelling process, the better cost estimation approach can be identified, and the movements of building costs are shown.

A continuous Deep Belief Network (cDBN) with two hidden layers is proposed in this paper, focusing on the problem of weak feature learning ability when dealing with continuous data. In cDBN, the input data is trained in an unsupervised way by using continuous version of transfer functions, the contrastive divergence is designed in hidden layer training process to raise convergence speed, an improved dropout strategy is then implemented in unsupervised training to realize features learning by de-cooperating between the units, and then the network is fine-tuned using back propagation algorithm. Besides, hyper-parameters are analysed through stability analysis to assure the network can find the optimal. Finally, the experiments on Lorenz chaos series, CATS benchmark and other real world like CO2 and waste water parameters forecasting show that cDBN has the advantage of higher accuracy, simpler structure and faster convergence speed than other methods.

Remote sensing plays a central role in the assessment of environmental phenomena and has increasingly become a powerful tool for monitoring shorelines, rivers morphology, flood waves delineation and floods assessment. Optical based monitoring and characterization of river evolution at long time scales is a key tool in fluvial geomorphology. However, the evolution occurring during extreme events is crucial for the understanding of the river dynamics under severe flow conditions and requires the processing of data from active sensors to overcome cloud obstructions. This work proposes a cloud-based unsupervised algorithm for the intra-event monitoring of river dynamics during extreme flow conditions based on time series of Sentinel-1 SAR data. The method allows the extraction of multi-temporal series of spatially explicit geometric parameters at high time and spatial resolutions, linking them to the hydrometric levels acquired by reference gauge stations. Intra-event reconstruction of inundation dynamics has led to the estimation of the relationship between hydrometric level and wet area extension and the assessment of bank erosion phenomena. Time series of SAR acquisitions, provided by Copernicus Sentinel-1 satellites, were analyzed to quantify changes in the wet area of a reach of the Tagliamento river under different flow conditions. The algorithm, developed within the Python-API of GEE, first empowers the Sentinel-1 images with the hydrometric level, then involves radiometric slope correction and speckle noise filtering. The Otsu method is then used for image segmentation leading to a water and dry land binary classification. Results support many types of analysis about river dynamics, including morphological changes, floods monitoring and relief efforts and bio-physical habitat dynamics. The results encourage future advancements and applications of the algorithm, specifically exploring SAR data from ICEYE and Capella Space constellations, which offer significantly higher spatial and temporal resolutions compared to Sentinel-1 data.

This paper addresses the evolving landscape of electricity markets in Europe, with a focus on the integration of Renewable Energy Communities as introduced by the Renewable Energy Directive 2018/2001. Residents within a postal code area are highly incentivized to join a community, which enables them to exchange energy among themselves at lower procurement costs. Thereby, energy management systems optimize the operation of respective energy systems, with electrical load forecasting playing a key role. Given that prosumers may switch between communities on a daily basis, electricity demands within these groups will vary, leading to data that is non-stationary, discontinuous as well as non-identical and independently distributed. To encounter this issue, we propose a sophisticated forecasting model that applies federated learning, using informations from various distributed communities to learn domain-invariant features. To achieve this, we initially utilize synthetic electrical load time series at district level and aggregate them to profiles of Renewable Energy Communities with dynamic portfolios. Subsequently, we develop a forecasting model that accounts for the composition of residents of a Renewable Energy Community, adapt data pre-processing in accordance with the time series process, and detail a federated learning algorithm that incorporates weight averaging and data sharing. Following the training of various experimental setups, we ultimately evaluate their effectiveness. The findings suggest that our proposed framework is capable of effectively forecast non-stationary and discontinuous time series and that it can be applied to new, unseen data through the integration of knowledge from multiple sources.

Landsat and Sentinel-2 data archives provide ever-increasing amounts of satellite data for studying land cover and land use change (LCLUC) over the past four decades. However, the availability of cloud-, shadow-, and snow-free observations varies spatially and temporally due to climate and satellite data acquisition schemes. Spatio-temporal heterogeneity poses a major issue for some time-series analysis approaches, but can be addressed with pixel-based compositing that generates temporally equidistant cloud-free or near-cloud free synthetic images. Although much consideration is given to methods identifying the ‘best’ pixel value for each composite, determining the aggregation period receives less attention and is often done arbitrary, or based on expert intuition. Here, we evaluated data compositing windows ranging from five days to one year for 1984-2021 Landsat and 2015-2021 Sentinel‑2 time series across Europe. We considered separate and joint use of both data archives and analyzed spatio-temporal availability of composites during each calendar year and pixel-specific growing season. We reported mean annual composites’ availability investigating differences among biogeographical regions, checked feasibility of pan‑European analyses for three LCLUC applications based on annual, monthly and 10-day composites, and analyzed the shortest feasible compositing window ensuring ≥50% temporal data availability and interpolation of the remaining composites for individual years and across a variety of medium- and long‑term time windows. Our results highlighted low data coverage in the 1980s, 1990s, and in 2012, as well as spatial variability in data availability driven by climate and orbit overlaps, which altogether impact spatio-temporal consistency of medium- and long-term time series, limiting feasibility of some LCLUC analyses. We demonstrated that prior to 2011 monthly composites ensured overall 50-62% data coverage for each calendar year, and ~75% afterwards, with further increase to ~82% when Landsat and Sentinel-2 were combined. Temporal consistency of monthly composites was overall low and temporal interpolation augmenting up to 50% missing data each year and across a time window of interest, ensured feasibility of analyses. Applications based on shorter than monthly composites were challenging without joining Landsat and Sentinel‑2 archives after 2015, and beyond the Mediterranean biogeographical region. Using pixel-specific growing season data typically boosted data availability in most geographies and diminished most of the latitudinal differences, but feasibility of complete time series with sub-monthly compositing windows was still restricted to the most recent years, and required data interpolation. Overall, our analyses provided a detailed assessment of Landsat and Sentinel-2 data availability over Europe, and based on selected application examples, highlighted often lacking spatio-temporal consistency of time series with sub-monthly compositing windows and long-time periods, which might hinder feasibility of some LCLUC applications.

This study considers the change-point test problem for time series based on the self-normalization ratio statistic test, which is constructed using residuals obtained from a support vector regression (SVR)-autoregressive moving average (ARMA) model. Under the null hypothesis, the series is a stationary process, and our test statistic converges to a non-degenerate distribution. Under the alternative hypothesis, there are change-points in the time series, and the self-normalization test statistic diverges to infinity. The simulations show that our proposed new test has better finite sample performance than other SVR-based tests in the literature. Finally, we illustrate its usefulness by analyzing two actual data sets.

Soybean maturity is a trait of critical importance for the development of new soybean cultivars, nevertheless, its characterization based on visual ratings has many challenges. Unmanned aerial vehicles (UAVs) imagery-based high-throughput phenotyping methodologies have been proposed as an alternative to the traditional visual ratings of pod senescence. However, the lack of scalable and accurate methods to extract the desired information from the images remains a significant bottleneck in breeding programs. The objective of this study was to develop an image-based high-throughput phenotyping system for evaluating soybean maturity in breeding programs. Images were acquired twice a week, starting when the earlier lines began maturation until the latest ones were mature. Two complementary convolutional neural networks (CNN) were developed to predict the maturity date. The first using a single date and the second using the five best image dates identified by the first model. The proposed CNN architecture was validated using more than 15,000 ground truth observations from five trials, including data from three growing seasons and two countries. The trained model showed good generalization capability with a root mean squared error lower than two days in four out of five trials. Four methods of estimating prediction uncertainty showed potential at identifying different sources of errors in the maturity date predictions. The architecture used solves limitations of previous research and can be used at scale in commercial breeding programs.

We consider the financial planning problem of a retiree wishing to enter a retirement village at a future uncertain date. The date of entry is determined by the retiree's utility and bequest maximisation problem within the context of uncertain future health states. In addition, the retiree must choose optimal consumption, investment, bequest and purchase of insurance products prior to her full annuitisation on entry to the retirement village. A hyperbolic absolute risk-aversion (HARA) utility function is used to allow necessary consumption for basic living and medical costs. The retirement village will typically require an initial deposit upon entry. This threshold wealth requirement leads to exercising the replication of an American put option at the uncertain stopping time. From our numerical results, active insurance and annuity markets are shown to be a critical aspect in retirement planning.

Background: Time-series biosignal data, representative of a physiological process, is often applied to time-sensitive machine learning applications that benefit from acceleration. Medical and research applications that process biosignal data in real-time may utilize new hardware architecture by switching from CPU to GPU devices to take advantage of the data processing speedups. In order to utilize machine learning kernels that are typically employed by a CPU on a GPU, the machine learning kernel must be reimplemented using custom compilers that can take advantage of GPU architecture. Objectives: The primary objective is to evaluate the speed of CPU-based machine learning algorithms commonly employed in biosignal process- ing and compare the speedup improvements obtained through GPU acceleration. Methods: A systematic search was conducted across multiple databases to identify studies employing GPU acceleration in biosignal processing. Inclusion and exclusion criteria are defined for GPU accel- eration studies. In this literature review, 12 studies of GPU kernel development for traditionally CPU-based kernels are analyzed. Results: It is found that a positive speedup occurs when using GPU kernels over traditional CPU-based algorithms in all instances. The speedup of GPU over CPU performance ranges between 1.87 to 27018.27 times faster. Conclusions: This review will contribute to the understanding of the role of GPU kernel development in biosignal processing, providing insights into performance improvements obtained by current GPU kernel development. The results indicate that GPU kernel development is a plausible direction to obtain real-time biosignal-based systems.

With the recent advances in Machine Learning (ML), several models have been successfully applied to financial and accounting data to predict the likelihood of companies’ bankruptcy. However, time series have received little attention in literature with a lack of studies on the application of Deep Learning sequence models as Recurrent Neural Networks (RNN) and the recent Attention-based models in general. In this research work, we investigated the application of Long Short Term Memory (LSTM) networks to exploit time series of accounting data for bankruptcy prediction. The main contributions of our work are the following: a) we have proposed a Multi-head LSTM that models each financial variable in a time window independently and compared it with a single-input LSTM and other traditional ML models. The Multi-head LSTM outperforms all the other models; b) We identify the optimal time series length for bankruptcy prediction to be equal to 4 years of accounting data; c) We made public the dataset we used for the experiments that include data from 8262 different public companies in the American stock market generated in the period between 1999-2018. Furthermore, we prove the efficacy of the Multi-head LSTM models in terms of lower false positives and better division of the two classes.

In this paper, we propose a method for assessing the effectiveness of entropy features using several chaotic mappings. We anlyze fuzzy entropy (FuzzyEn) and neural network entropy (NNetEn) on four discrete mappings: the logistic map, the sine map, the Planck map, and the two-memristor-based map, with a base length time series of 300 elements. FuzzyEn is shown to have improved global efficiency (GEFMCC) in the classification task compared to NNetEn. At the same time, there are local areas of the time series dynamics in which the classification efficiency NNetEn is higher than FuzzyEn. The results of using horizontal visibility graphs (HVG) instead of the raw time series are also shown. GEFMCC decreases after HVG time series transformation, but there are local areas of the time series dynamics in which the classification efficiency increases after including the HVG. The scientific community can use the results to explore the efficiency of entropy-based classification of time series.

Purpose To alleviate the data imbalance problem caused by subjective and objective reasons, scholars have developed different data preprocessing algorithms, among which undersampling algorithms are widely used because of their fast and efficient performance. However, when the number of samples of some categories in a multi-classification dataset is too small to be processed by sampling, or the number of minority class samples is only 1 to 2, the traditional undersampling algorithms will be weakened. Methods This study selects 9 multi-classification time series datasets with extremely few samples as the objects, fully considers the characteristics of time series data, and uses a three-stage algorithm to alleviate the data imbalance problem. Stage one: Random oversampling with disturbance items increases the number of sample points; Stage two: On this basis, SMOTE (Synthetic Minority Oversampling Technique) oversampling; Stage three: Using dynamic time warping distance to calculate the distance between sample points, identify the sample points of Tomek Links at the boundary, and clean up the boundary noise.Results This study proposes a new sampling algorithm. In the 9 multi-classification time series datasets with extremely few samples, the new sampling algorithm is compared with four classic undersampling algorithms, ENN (Edited Nearest Neighbours), NCR (Neighborhood Cleaning Rule), OSS (One Side Selection) and RENN (Repeated Edited Nearest Neighbours), based on macro accuracy, recall rate and F1-score evaluation indicators. The results show that: In the 9 datasets selected, the dataset with the most categories and the least number of minority class samples, FiftyWords, the accuracy of the new sampling algorithm is 0.7156, far beyond ENN, RENN, OSS and NCR; its recall rate is also better than the four undersampling algorithms used for comparison, at 0.7261; its F1-score is increased by 200.71%, 188.74%, 155.29% and 85.61%, respectively, relative to ENN, RENN, OSS, and NCR; In the other 8 datasets, this new sampling algorithm also shows good indicator scores.Conclusion The new algorithm proposed in this study can effectively alleviate the data imbalance problem of multi-classification time series datasets with many categories and few minority class samples, and at the same time clean up the boundary noise data between classes.

We propose a novel tensor-based formalism for inferring causal structures from time series. An information theoretical analysis of transfer entropy (TE), shows that TE results from transmission of information over a set of communication channels. Tensors are the mathematical equivalents of these multi-channel causal channels. A multi-channel causal channel is a generalization of a discrete memoryless channel (DMC). We consider a DMC as a single-channel causal channel. Investigation of a system comprising three variables shows that in our formalism, bivariate analysis suffices to differentiate between direct and indirect relations. For this to be true, we have to combine the output of multi-channel causal channels with the output of single-channel causal channels. We can understand this result when we consider the role of noise. Subsequent transmission of information over noisy channels can never result in less noisy transmission overall. This implies that a Data Processing Inequality (DPI) exists for transfer entropy.

Satellite Crop Detection technologies are focused on detection of different types of crops on the field in the early stage before harvesting. Crop detection is usually done on a time series of satellite data by classification of the desired fields. Currently, data obtained from Remote Sensing (RS) are used to solve tasks related to the identification of the type of agricultural crops, also modern technologies using AI methods are desired in the postprocessing part. In this challenge Sentinel-1 and Sentinel-2 time series data were used due to their periodic availability. Our focus was to develop methodology for classification of time series of Sentinel 2 and Sentinel 1 data and compare how accuracy of classification can be increased, but also how to guarantee availability of data. We analyse phenology of single crops and on the basis of this analysis we started to provide crop classification. Original crop classifications were made from Enhanced Vegetation Index (EVI) layers made from Sentinel-2 time-series data and then we added also . To increase accuracy we also integrate into the process parcel borders and provide classification of fields..

Mapping forest extent and forest cover classification are important for the assessment of forest resources in socio-economic as well as ecological terms. Novel developments in the availability of remotely sensed data, computational resources, and advances in areas of statistical learning have enabled fusion of multi-sensor data, often yielding superior classification results. Most former studies of nemoral forests fusing multi-sensor and multi-temporal data have been limited in spatial extent and typically to a simple classification of landscapes into major land cover classes. We hypothesize that multi-temporal, multi-censor data will have a specific strength in further classification of nemoral forest landscapes owing to the distinct seasonal patterns of the phenology of broadleaves. This study aimed to classify the Danish landscape into forest/non-forest and further into forest types (broadleaved/coniferous) and species groups, using a cloud-based approach based on multi-temporal Sentinel 1 and 2 data and machine learning (random forest) trained with National Forest Inventory (NFI) data. Mapping of non-forest and forest resulted in producer accuracies of 99% and 90 %, respectively. The mapping of forest types (broadleaf and conifer) within the forested area resulted in producer accuracies of 95% for conifer and 96% for broadleaf forest. Tree species groups were classified with producer accuracies ranging 34-74%. Species groups with coniferous species were the least confused whereas the broadleaf groups, especially Oak, had higher error rates. The results are applied in Danish National accounting of greenhouse gas emissions from forests, resource assessment and assessment of forest biodiversity potentials.

Accurately predicting electrical signals of three-phase Direct Torque Control (DTC) induction motors is crucial for optimal motor performance and effective condition monitoring. However, multiple DTC motors’ complexity and operating conditions’ variations pose challenges for traditional prediction methods. To overcome these challenges, we propose an innovative approach that combines Fast Fourier Transform (FFT) to transform electrical motor simulation data and a Bi-directional Long Short-Term Memory (Bi-LSTM) network to forecast processed motor data. By transforming the DTC induction motor signals from the time domain to the frequency domain, we enhance the capability of learning models to capture subtle differences and generate various input features. The Bi-LSTM model effectively captures both forward and backward dependencies in time series data, enabling accurate prediction of electrical signals. We evaluate the proposed approach using our simulated dataset and compare the proposed method to a state-of-the-art model, the Gated Recurrent Unit (GRU), demonstrating its effectiveness in improving the accuracy and reliability of induction motor signals forecasting. The finding provides valuable insights for advancing motor control and operation in industrial applications.

In this study, UAV (Unmanned Aerial Vehicle) photogrammetry was used to monitor the ground displacement on the slope below a coal waste-rock stockyard, and to investigate the role of rainfall on this displacement. The study area is a mountainous region in Korea, where coal mining continues, and coal waste-rock is stored on the slopes of the mountain. In this area, ma-terial removal work was undertaken to reduce the steepness of the slope and driving forces in order to prevent disasters, but the strategy requires continuous monitoring to confirm the stabilization of the slope. For slope monitoring, a total of six UAV photogrammetry campaigns were conducted between April 2019 and August 2020. As a result of data processing, an orthoimage and DSM (Digital Surface Model) were generated. The ground displacement was estimated through four ways: slope extraction, displacement area evaluation, horizontal displacement, and vertical displacement analysis. During the study period, the maximum vertical displacement was 3.3 m and the maxi-mum horizontal displacement was 3.5 m. The horizontal displacement was effectively evaluated through the measurement of the movement of the drainage system using orthoimages that captured with a periodic survey. The effects of rainfall on ground displacement were also investigated. A very clear linear relationship between rainfall intensity higher than 20mm/d and ground displacement was identified. Accumulated amount of rainfall also showed good correlation with slope movement, but the frequency of rainfall intensity below 20 mm/d showed relatively low correlation with ground dis-placements.

We have implemented quantum modeling mainly based on Bohmian Mechanics to study time series that contain strong coupling between their events. Compared to time series with normal densities, such time series are associated with rare events. Hence, employing Gaussian statistics drastically underestimates the occurrence of their rare events. The central objective of this study is to investigate the effects of rare events in the probability densities of time series from the point of view of quantum measurements. For this purpose, we first model the non-Gaussian behavior of time series using the multifractal random walk (MRW) approach. Then, we examine the role of the key parameter of MRW, λ, which controls the degree of non-Gaussianity, in quantum potentials derived for time series. Our Bohmian quantum analysis shows that the derived potential takes some negative values in high frequencies (its mean values), then substantially increases, and the value drops again for rare events. Thus, rare events can generate a potential barrier in the high-frequency region of the quantum potential, and the effect of such a barrier becomes prominent when the system transverses it. Finally, as an example of applying quantum potential beyond the microscopic world, we compute quantum potentials for the S&P financial market time series to verify the presence of rare events in the non-Gaussian densities and demonstrate deviation from the Gaussian case.

Background: The current coronavirus disease 2019 (COVID-19) is spreading globally at an accelerated rate. There is some previous evidence that weather may influence the incidence of COVID-19 infection. We assessed the role of meteorological factors including temperature (T) and relative humidity (RH) considering the concentrations of two air pollutants, inhalable coarse particles (PM10) and nitrogen dioxide (NO2) in the incidence of COVID-19 infections in Finland, located in arctic-subarctic climatic zone. Methods: We retrieved daily counts of COVID-19 in Finland from Jan 1 to May 31, 2020, nationwide and separately for all 21 hospital districts across the country. The meteorological and air quality data were from the monitoring stations nearest to the central district hospital. A quasi-Poisson generalized additional model (GAM) was fitted to estimate the associations between district-specific meteorological factors and the daily counts of COVID-19 during the study period. Sensitivity analyses were conducted to test the robustness of the results. Results: The incidence rate of COVID-19 gradually increased until a peak around April 6 and then decreased. There were no associations between daily temperature and incidence rate of COVID-19. Daily average RH was negatively associated with daily incidence rate of COVID-19 in two hospital districts located inland. No such association was found nationwide. The sensitivity analyses indicate the results are robust. Conclusions: Weather conditions, such as air temperature and relative humidity, may not be important factors affecting the COVID-19 incidence in the arctic and subarctic winter and spring. More evidence is needed on the associations between weather and COVID-19 during different seasons.

Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for a) describing the dynamics and b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and non-linearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of non-linearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics.

Changes in sea level exhibit nonlinearity, nonstationarity, and multivariable characteristics, making traditional time series forecasting methods less effective in producing satisfactory results. To enhance the accuracy of the predictions of changes in sea level, this study introduced an improved VMD–EEMD–LSTM hybrid model. This model decomposes satellite altimetry data from near the Dutch coast using VMD, resulting in components of the Intrinsic Mode Function (IMF) with various frequencies and a residual sequence. EEMD further dissects the residual sequence obtained from VMD into second-order components. These IMFs decomposed by VMD and EEMD are utilized as features in the LSTM model for making predictions, culminating in the final forecasted results. The experimental results demonstrated significant improvements in the predictive performance compared with the VMD–LSTM model. The RMSE (root mean square error) decreased by an average of 58.68%, the MAE (mean absolute error) reduced by an average of 59.96%, and the R2 (coefficient of determination) increased by an average of 49.85% compared with the VMD–LSTM model. In comparison with the EEMD–LSTM model, the RMSE decreased by an average of 26.95%, the MAE decreased by an average of 28.00%, and the R2 increased by an average of 6.53%. The VMD–EEMD–LSTM model exhibited significantly improved predictive performance.

Accurate prediction of crop production is essential in effectively managing agricultural countries' food security and economic resilience. This study evaluates the performance of statistical and machine learning-based methods for large-scale crop production forecasting. We predict the quarterly production of 325 crops (including fruits, vegetables, cereals, non-food, and industrial crops) across 83 provinces in the Philippines. Using a comprehensive dataset of 10,949 time series over 13 years, we demonstrate that a global forecasting approach using a state-of-the-art deep learning architecture, the transformer, significantly outperforms traditional local forecasting approaches built on statistical and baseline methods. By leveraging cross-series information, our proposed way is scalable and works well even with time series that are short, sparse, intermittent, or exhibit structural breaks/regime shifts. The results of this study further advance the field of applied forecasting in agricultural production and provide a practical and effective decision-support tool for policymakers that oversee the farm sector on a national scale.

Time series (TS)-based predictions are made by examining the behaviour of historical data to forecast future values. Multiple industries; such as stock market trading, power load forecasting, medical monitoring, and intrusion detection; frequently use it. Several variables; such as the performance of other markets as well as the economic situation of a country which affect its market performance; significantly affect the prediction of stock market prices. Therefore, this present study uses numerous variables; such as the opening, lowest, highest, and closing prices; to predict the indices of the stock market of the Kingdom of Saudi Arabia (KSA). Successfully accomplishing an investment goal largely depends on choosing the right stocks to buy, sell, or maintain. The project's output is the projected closing prices (regression) over the next seven days, which helps investors make the best decisions. This present study used exponential smoothing (ES) to remove noise from the input data obtained from the Saudi Stock Exchange, or Tadawul, before using a multivariate long short-term memory (LSTM) deep learning (DL) algorithm to forecast stock market prices. The proposed multivariate LSTMDL model had satisfactory prediction rates of 97.49% and 92.19% for the univariate model. Therefore, it can be used to effectively predict stock market prices. The results also indicate that DL as well as multiple sources of information can be used to accurately predict stock markets.

The global threat of COVID-19 has led to the increasing use of metabolomics to study SARS-CoV-2 infection in humans and animals. Despite this, understanding SARS-CoV-2's metabolome during infection remains difficult and incomplete. Here, metabolic responses were characterized from sampled nasal washes collected from an asymptomatic ferret model (n = 20) at different time points before and after the SARS-CoV-2 challenge using an LC-MS-based metabolomics approach. Multivariate analysis of the nasal wash metabolome data resulted in several statistically significant features being observed. Despite no effects of gender or interaction between gender and time on the time course of SARS-CoV-2 infection, 16 metabolites were significantly different at every time point post-infection. Among these altered metabolites, the relative abundance of taurine was elevated post infection which could be an indication of hepatotoxicity, while the accumulation of sialic acids could indicate SARS-CoV-2 invasion. The pathway analysis identified several pathways influenced by SARS-CoV-2 infection. Of these, sugar, glycan, and amino acid metabolisms were the key altered pathways in the upper respiratory channel during infection. These findings provide some new insights into the progression of SARS-CoV-2 infection in ferrets at the metabolic level which could be useful for the development of early clinical diagnosis tools and new or repurposed drug therapies.

Extensive, but remote oil and gas fields of the United States, Canada, and Russia require the construction and operation of extremely long pipelines. Global warming and local heating effects lead to rising soil temperatures and thus a reduction in the sub-grade capacity of the soils; this causes changes in the spatial positions and forms of the pipelines, consequently increasing the number of accidents. Oil operators are compelled to monitor the soil temperature along the routes of the remoted pipelines in order to be able to perform remedial measures in time. They are therefore seeking methods for the analysis of volumetric diagnostic information. To forecast soil temperatures at the different depths we propose compiling a multidimensional dataset, defining descriptive statistics; selecting uncorrelated time series; generating synthetic features; robust scaling temperature series, tuning the additive regression model to forecast soil temperatures.

(1) Introduction: The unprecedented coronavirus disease 2019 (COVID-19) epidemic has caused millions of infections worldwide and represents a significant challenge facing modern health care systems. This study was conducted to investigate the impact of lockdown measures on regional neonate services, which might be used to predict the long-term effects of medical behavior. (2) Methods: Using hospital information system (HIS) Statistics data from 4 January 2019 to 27 August 2020, an interrupted time-series analysis was employed to compare changes and trends in hospital admissions and disease spectrum before and after the lockdown interventions. Furthermore, this study was designed to evaluate whether the pandemic influenced newborns' healthcare behavior. (3) Results: Overall, 13,540 infants were admitted to the NICU during the pre-COVID period (n = 12082) and COVID-impacted period (n =4558). The patients' age at admission were younger than that of the pre-COVID-19 period (median age 5d vs. 6d after birth, p＜0.001). The overall number of neonate visits consistently decreased from the first days of the lockdown measures (24 January 2020). The disease spectrum for respiratory system, infectious diseases, and gastrointestinal disease indicated no declined immediately after intervention(p =0.079, p =0.113, p =0.060, respectively). There was an immediate decline in the volume of Jaundice-related conditions (p<0.001) after lockdown measures. The percentage of patients who suffer from respiratory system and infectious diseases has decreased (p =0.005 and p =0.002). However, a relatively high percentage of patients admitted to the neonatal intensive care unit (NICU) presented with Jaundice-related conditions (p <0.001). (4) Conclusions: In summary, the COVID-19 pandemic profoundly impacted the regional neonate services. However, it is still unclear what might be the effect of long-term effects from pandemic.

Wearable sensors have the potential to enable comprehensive patient characterization and optimized clinical intervention. Critical to realizing this vision is accurate estimation of biomechanical time-series in daily-life, including joint, segment, and muscle kinetics and kinematics, from wearable sensor data. The use of physical models for estimation of these quantities often requires many wearable devices making practical implementation more difficult. However, regression techniques may provide a viable alternative by allowing the use of a reduced number of sensors for estimating biomechanical time-series. Herein, we review 46 articles that used regression algorithms to estimate joint, segment, and muscle kinematics and kinetics. We present a high-level comparison of the many different techniques identified and discuss the implications of our findings concerning practical implementation and further improving estimation accuracy. In particular, we found that several studies report the incorporation of domain knowledge often yielded superior performance. Further, most models were trained on small datasets in which case nonparametric regression often performed best. No models were open-sourced, and most were subject-specific and not validated on impaired populations. Future research should focus on developing open-source algorithms using complementary physics-based and machine learning techniques that are validated in clinically impaired populations. This approach may further improve estimation performance and reduce barriers to clinical adoption.

The future of the Colorado River water supply (WS) affects millions of people and the U.S. economy. A recent study suggested a cross-basin correlation between the Colorado River and its neighboring Great Salt Lake (GSL). Following that study, the feasibility of using the previously developed multi-year prediction of the GSL water level to forecast the Colorado River WS was tested. Time-series models were developed to predict the changes in WS out to 10 years. Regressive methods and the GSL water level data were used for the depiction of decadal variability of the Colorado River WS. Various time-series models suggest a decline in the 10-year-averaged WS since 2013 before starting to increase around 2020. Comparison between this WS prediction and the WS projection published in a 2012 government report (derived from climate models) reveals a widened imbalance between supply and demand by 2020. Further research to update similar multi-year prediction of the Colorado River WS is needed. Such information could aid in management decision making in the face of future water shortages.

In the paper, the authors discover several series identities involving the Catalan numbers, the Catalan function, the Riemanian zeta function, and the alternative Hurwitz zeta function.

Catastrophic mass flows originating from the high mountain cryosphere often cause hazard cascades. With increasing human activities in the alpine region and the sensitivity of glaciers, snow and permafrost to climate warming, the cryospheric hazard risks tend to be more active in the Tibetan Plateau(TP). The remoteness and inaccessibility of high mountain regions make the remote sensing technology the most effective approach for monitoring and investigating the cryospheric hazards. Exploring the evolution process and impact of ice avalanches and subsequent hazards are crucial to understand drivers and nature of mass flow process chain in order to prevent and mitigate potential hazard consequences. In this study, the glacier and ice-rock avalanches occurred in Arutso and Sedongpu basins in Tibet were investigated on the basis of Sentinel-2 time-series images and in-situ investigation, the evolution process of these events were reconstructed, and impacts and driving factors were analyzed. The massive Chamoli rock-ice avalanche occurred in February 2021 in the western Himalayas was also reviewed using using same methods. The study shows that Arutso glacier No. 53 (Arutso-53) avalanche completely melted away in July 2018 after two years from occurrence to final disappearance, while Arutso glacier No. 50 (Arutso-50) avalanche completely melted by the end of August 2023 after lasting for seven years. Four large-scale ice-rock avalanche and debris flow events in the Sedongpu basin in 2017 and 2018 not only had significant impacts on the river flow, landscape and geomorphologic shape in the basin, but also caused serious disasters in the basin and downstream. In March 2021, a small-scale ice-rock avalanche and debris flow event occurred again in the Sedongpu basin. The glacier and ice-rock avalanches occurred in Tibet area were mainly induced by climate warming, heavy precipitation and seismic activity, which acting on specific topographic and geomorphic structure of glacier properties in the high mountain regions. Catastrophic hazard events originating from the high-elevation glacier and ice-rock collapses in the mountain cryosphere and subsequent hazard cascades in the TP and Himalayas highlight the importance of mountain hazard monitoring, early warning systems and sustainable mountain development.

Fractal analysis of time series aims to extract the hidden or complex structures issued from the associated real data, such as scaling laws, non-stationary, dynamics, and so on. In the present work, the air quality index and its components are considered as time series owing fractal structures. To understand their underlying dynamics, wavelet multifractal approach is applied starting with a wavelet multifractal spectrum test to confirm the multifractality of the underlying data. Next, a new model is introduced improving the classical minmax one, provided with a statistical measure for the adequacy of the new model. The theoretical findings are applied to the north west Tabuk region of Saudi Arabia for environmental and climate data related to pollutants and factors involved in the estimation of the air quality index.

Today, there is a time series analysis that has gained significant popularity across various industries to provide effective solutions for any specific challenges. Artificial intelligence logic is generally used to solve time-series problems with the help of various frameworks that are available for the development of AI-based applications. Currently, there is a significant framework in Python that is driven by its comprehensive libraries and their practical implementations. Time series analysis can be built with the help of some specific models that give results to differentiate the efficiency and domains of great work. This paper focuses on three diverse libraries of Python to predict the Gulf stock exchange market. These libraries are prediction models that are helpful in predicting future values. These models utilized include SARIMA (Seasonal Auto-Regressive Integrated Moving Average), Neural Prophet Model, and Fb Prophet model. Each model is trained using the provided datasets, which are followed by evaluation parameters such as MSE, RMSE, recall, MDAPE, accuracy, precision, etc. The main purpose of using these three models for stock market prediction is to find the better-suited models. In the past few decades, the stock market industry has seemed to have promising growth after 2022 onwards. This paper will help us make a significant decision about model usage for addressing such complex challenges. Especially, the research findings indicate that all three models demonstrate in different domains. SARIMA can perform well in overall prediction tasks, while the Prophet model works great with smaller datasets that contain seasonality trends.

For more than half a century, Manfred Deistler has been contributing to the construction of the rigorous theoretical foundations of the statistical analysis of time series and more general stochastic processes. Half a century of unremitting activity is not easily summarized in a few pages. In this short note, we chose to concentrate on a relatively little-known aspect of Manfred's contribution which nevertheless had quite an impact on the development of one of the most powerful tools of contemporary time series and econometrics: dynamic factor models.

Traditional methodologies for measuring combat effectiveness rely on various contribution factors, where the main challenge lies in the complexity and subjectivity of these factors. Using frontline variation to measure combat effectiveness circumvents the limitations of many previous methods regarding complexity and subjectivity. Employing this methodology, we have quantitatively measured the combat effectiveness of both parties in the Russo-Ukrainian War across various temporal scales. Utilizing the time series data derived from our measurements, we constructed Daily, Weekly, Monthly, and Annual Candlestick Charts to illustrate the variation trends in combat effectiveness between the two sides across different temporal scales. This comprehensive approach facilitated a nuanced and all-encompassing analysis of the conflict, capturing the intricate dynamics of individual military engagements and the broader strategic operations' context. This case underscores the distinctive utility of our method in quantifying combat effectiveness, offering detailed and strategically significant insights.

To improve the monitoring of the electrical power grid it is necessary to evaluate the influence of contamination in relation to leakage current and its progression to a disruptive discharge. In this paper, insulators were tested in a saline chamber to simulate the increase of salt contamination on their surface, and to evaluate the supportability of these components. From the time series forecasting of the leakage current, it is possible to evaluate the development of the fault before a flashover occurs. Choosing which method to use is always a difficult task since some models may have higher computational effort. In this paper, for a complete evaluation, the long short-term memory (LSTM), group method of data handling (GMDH), adaptive neuro-fuzzy inference system (ANFIS), bootstrap aggregation (bagging), sequential learning (boosting), random subspace, and stacked generalization (stacking) ensemble learning models are analyzed. A review and comparison of these well-established methods for time series forecasting is performed. From the results of the best structure of the model, the hyperparameters are evaluated and the Wavelet transform is used to obtain an enhanced model.

This paper proposes a forecast-centric adaptive learning model that engages with the past studies on the order book and high-frequency data, with applications to hypothesis testing. In line with the past literature, we produce brackets of summaries of statistics from the high-frequency bid and ask data in the CSI 300 Index Futures market and aim to forecast the one-step-ahead prices. Traditional time series issues, e.g. ARIMA order selection, stationarity, together with potential financial applications are covered in the exploratory data analysis, which pave paths to the adaptive learning model. By designing and running the learning model, we found it to perform well compared to the top fixed models, and some could improve the forecasting accuracy by being more stable and resilient to non-stationarity. Applications to hypothesis testing are shown with a rolling window, and further potential applications to finance and statistics are outlined.

In Portugal, cork oak (Quercus suber L.) stands cover 737 Mha, being the most predominant species of the montado agroforestry system, contributing for the economic, social and environmental development of the country. Cork oak decline is a known problem since the late years of the 19th century that has recently worsen. The causes of oak decline seem to be a result of slow and cumulative processes, although the role of each environmental factor is not yet established. The availability of Sentinel-2 high spatial and temporal resolution dense time series enables gradual processes monitoring. These processes can be monitored using spectral vegetation indices (VI) once their temporal dynamics are expected to be related with green biomass and photosynthetic efficiency. The Normalized Difference Vegetation Index (NDVI) is sensitive to structural canopy changes, however it tends to saturate at moderate-to-dense canopies. Modified VI have been proposed to incorporate the reflectance in the red-edge spectral region, which is highly sensitive to chlorophyll content while largely unaffected by structural properties. In this research, in-situ data on the location and vitality status of cork oak trees are used to assess the correlation between chlorophyll indices (CI) and NDVI time series trends and cork oak vitality at the tree level. Preliminary results seem to be promising since differences between healthy and unhealthy (diseased/dead) trees were observed.

Soybean yields are often indicated as an interesting case of climate change mitigation due to the beneficial effects of CO₂ fertilization. In this paper we econometrically study this effect using a time series model of yields in a multivariate framework for a main producer and exporter of this commodity, Argentina. We have to deal with the upward behavior of soybean yields trying to identify which variables are the long-run determinants responsible of its observed trend. With this aim we adopt a partial system approach to estimate subsets of long-run relationships due to climate, technological and economic factors. Using an automatic selection algorithm we evaluate encompassing of the different obtained equilibrium correction models. We found that only technological innovations due to new crop practices and the use of modified seeds explain soybean yield in the long run. Regarding short run determinants we found positive effects associated with the use of standard fertilizers and also from changes in atmospheric CO₂ concentration which would suggest a mitigation effect from global warming. However, we also found negative climate effects from periods of droughts associated with La Niña episodes, high temperatures and extreme rainfall events during the growing season of the plant.

Gait is a basic cognitive propositive action that has been shown to be altered in late stages of neurodegenerative dementias. Nevertheless, alterations are less clear in mild forms of dementia, and the potential use of gait analysis as a biomarker of initial cognitive decline has hitherto mostly been neglected. We here report the results of a study of gait kinematic time series for two groups of patients (Mild Cognitive Impairment and mild Alzheimer's disease) and a group of matched control subjects. Two metrics based on permutation patterns are considered, respectively measuring the complexity and irreversibility of the time series. Results indicate that kinematic disorganisation is present at early phases of cognitive impairment; in addition, they depict a rich scenario, in which some joint movements display an increased complexity and irreversibility, while others a marked decrease. Beyond their potential use as biomarkers, complexity and irreversibility metrics can open a new door towards the understanding of the role of the nervous system in gait, as well as its adaptation and compensatory mechanisms.

The aim of this study was to assess the ability of multiscale sample entropy (MSE), refined composite multiscale entropy (RCMSE), and complexity index (CI) to characterize gait complexity through trunk acceleration patterns in subjects with Parkinson's disease (swPD) and healthy subjects, regardless of age or gait speed. The trunk acceleration patterns of 51 swPD and 50 HS were acquired using a lumbar-mounted magneto-inertial measurement unit during their walking. MSE, RCMSE, and CI were calculated on 2000 data points, using scale factors (τ) 1-6. Differences between swPD and HS were calculated at each τ, and the area under the receiver operating characteristics, optimal cutoff points, post-test probabilities, and diagnostic odds ratios were calculated. MSE in the antero-posterior direction at τ 4 and τ 5, and MSE in the ML direction at τ 4 outperformed the other entropy measures in terms of discriminative ability and characterized the gait of swPD with 79%, 82%, and 78% probabilities, respectively, and correlated with the motor disability, pelvic kinematics, and stance phase. Using a time series of 2000 data points, a scale factor of 4 or 5 in the MSE procedure can be considered as a marker of gait variability and complexity in swPD.

Abstract: This paper presents a comprehensive analysis of links between satellite-measured vegetation vigor and climate variables in Armenian mountain grassland ecosystems in years 1984–2018. NDVI is derived from MODIS and Landsat data, temperature and precipitation data are from meteorological stations. Two study sites were selected, representing arid and semi-arid grassland vegetation types, respectively. Various trend estimators including Mann-Kendall (MK) and derivatives were combined for vegetation change analysis at different time scales. Results suggest that temperature and precipitation had negative and positive impacts on vegetation growth, respectively, in both areas. NDVI-to-precipitation correlation was significant but with an apparent time-lag effect that was further investigated. No significant general changes were observed in vegetation along the observed period. Further comparisons between results from corrected and uncorrected data led us to conclude that MODIS and Landsat data with BRDF, topographic and atmospheric corrections applied are best suited for analyzing relationships between NDVI and climatic factors for the 2000-2018 period in grassland at a very local scale, but in the absence of correction tools and information, uncorrected data can still provide meaningful results. Future refinements will include removal of anthropogenic impact, and deeper investigation of time-lag effects of climatic factors on vegetation dynamics.

Satellite Image Time Series (SITS) is a data set which includes satellite images across several years with a high acquisition rate. Radiometric normalization is a fundamental and important preprocessing method for remote sensing applications using SITS due to the radiometric distortion caused by noise between images. Normalizing the subject image based on the reference image is a general strategy when using traditional radiometric normalization methods to normalize multi-temporal imagery (usually two scenes or three scenes in different time phases). However, these methods are not suitable for calibrating SITS because they cannot minimize the radiometric distortion between any pair of images in SITS. The existing relative radiometric normalization methods for SITS are based on linear assumptions which cannot effectively reduce nonlinear radiometric distortion caused by continuously changing noise in SITS. To overcome this problem and obtain a more accurate SITS, this study proposed a Nonlinear Radiometric Normalization Model (named NMAG) for SITS based on Artificial Neural Networks (ANN) and Greedy Algroithm (GA) . In this method, GA was used to determine the correction order of SITS and calculate the error between the image to be corrected and normalized images, which avoided the selection of a single reference image. ANN was used to obtain the optimal solution of error function, which minimized the radiometric distortion between different images in SITS. SITS composed of 21 Landsat-8 images in Tianjin City from October 2017 to January 2019 were selected to test the method. We compared NMAG with other two contrasting method (refered as CM1 and CM2), and found that the average of root mean square error $(\mu_{RMSE})$ of NMAG $(497.22)$ was significantly smaller than those of CM1 $(641.39)$ and CM2 $(543.47)$, and the accuracy of normalized SITS obtained by using NMAG has increased by 22.4\% and 8.5\% toward CM1 and CM2, respectively. These experimental results confirmed the effectiveness of NMAG in the reduction of radiometric distortion caused by continuously changing noise between images in SITS.

Sharding shows great potential for extending the blockchain. The current challenge facing sharded blockchain technology lies in addressing the extended transaction confirmation times caused by isolated states between shards and unbalanced transaction allocation strategies. These factors contribute to an increase in cross-shard transactions and disproportionate shard workload, ultimately resulting in indefinite confirmation delays for cross-shard transactions. A critical priority for sharded blockchain systems is to conduct a comprehensive qualitative analysis to better understand and mitigate the prolonged transaction confirmation times. We introduce a Product-Form Queue Network (PFQN) model to address the transaction confirmation time problem in sharded blockchains and incorporate a new confirmation queue to more accurately simulate the actual transaction confirmation process in the blockchain. In addition, we provide a detailed quantitative analysis of the relationship between network load, consensus efficiency, and security in sharded blockchains, laying a theoretical foundation for achieving robustness and efficiency in sharded blockchains. This research not only contributes to addressing the scalability issues in sharded blockchains but also offers a new perspective for future research directions.

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

The necessity for precise and current data concerning the dynamics of land cover change in Indonesia is crucial for efforts to reduce natural vegetation cover due to agricultural expansion. The functionality of monitoring systems that incorporate Terra-MODIS is currently compromised by the limited availability of data for the immediate future. This study seeks to assess the potential of VIIRS satellite imagery in developing an early warning system for monitoring vegetation cover change in Indonesia. The Normalized Differential Open Area Index (NDOAI) computed from the 8-day’ VIIRS data was employed to detect changes in vegetation cover based on pixel-by-pixel subtraction in the NDOAI data time series. Evaluating the pixel-level accuracy of change detection is complicated due to the fact that we evaluate a change map at a coarser resolution than the Landsat-based reference map. The results revealed that increasing the threshold percentage is associated with improved accuracy. In change detection, there is often a trade-off between accuracy and sensitivity. A threshold that is too low may result in false positives, while a threshold that is too high may lead to missed changes. This study demonstrates that when a threshold value of less than 20% is applied, Landsat can identify vegetation cover changes at an earlier stage. Conversely, when a threshold value greater than 20% is employed, VIIRS will detect the change 4.5 days earlier than Landsat. Additionally, VIIRS is capable of detecting changes 25.4 days and 54.8 days faster than Landsat, respectively, when using thresholds of 40% and 75%.

Solar flares are characterized by sudden bursts of electromagnetic radiation from the Sun’s surface, and caused by the changes in magnetic field states in solar active regions. Earth and its surrounding space environment can suffer from various negative impacts caused by solar flares ranging from electronic communication disruption to radiation exposure-based health risks to the astronauts. In this paper, we address the solar flare prediction problem from magnetic field parameter-based multivariate time series (MVTS) data using multiple state-of-the-art machine learning classifiers that include MINImally RandOm Convolutional KErnel Transform (MINIROCKET), Support Vector Machine (SVM), Canonical Interval Forest (CIF), Multiple Representations SEQuence Learner (Mr-SEQL), and Long Short-Term Memory (LSTM)-based deep learning model. Our experiment is conducted on the on the Space Weather ANalytics for Solar Flares (SWAN-SF) benchmark data set, which is a partitioned collection of MVTS data of active region magnetic field parameters spanning over 9 years of operation of the Solar Dynamics Observatory (SDO). The MVTS instances of the SWAN-SF dataset are labeled by GOES X-ray flux-based flare class labels, and attributed to extreme class imbalance because of the rarity of the major flaring events (e.g., X and M). As a performance validation metric in this class-imbalanced dataset, we used the true skill statistic (TSS) score. Finally, we demonstrate the advantages of the MVTS learning algorithm MINIROCKET, which outperformed the aforementioned classifiers without the need for essential data preprocessing steps such as normalization, statistical summarization, and class imbalance handling heuristics.

The global demand for energy has been steadily increasing due to population growth, urbanization, and industrialization. Numerous researchers worldwide are striving to create precise forecasting models for predicting energy consumption to manage supply and demand effectively. In this research, a time-series forecasting model based on multivariate multilayered long short-term memory (LSTM) is proposed for forecasting energy consumption and tested using data obtained from commercial buildings in Melbourne, Australia: the Advanced Technologies Center, Advanced Manufacturing and Design Center, and Knox Innovation, Opportunity, and Sustainability Center buildings. This research specifically identifies the best forecasting method for subtropical conditions and evaluates its performance by comparing it with the most used methods at present, including LSTM, bidirectional LSTM, and linear regression. The proposed multivariate multilayered LSTM model was assessed by comparing mean average error (MAE), root-mean-square error (RMSE), and mean absolute percentage error (MAPE) values with and without labeled time. Results indicate that the proposed model exhibits optimal performance with improved precision and accuracy. Specifically, the proposed LSTM model achieved a decrease in MAE by 30%, RMSE by 25%, and MAPE by 20% compared to the LSTM method. Moreover, it outperformed the bidirectional LSTM method with a reduction in MAE by 10%, RMSE by 20%, and MAPE by 18%. Furthermore, the proposed model surpassed linear regression with a decrease in MAE by 2%, RMSE by 7%, and MAPE by 10%. These findings highlight the significant performance increase achieved by the proposed multivariate multilayered LSTM model in energy consumption forecasting.

The local reactive power control in distribution grids with a high penetration of distributed energy resources (DERs) is essential in future power system operation. Appropriate control characteristic curves for DERs support stable and efficient distribution grid operation. However, the current practice is to configure local controllers collectively with constant characteristic curves that may not be efficient for volatile grid conditions or the desired targets of grid operators. To address this issue, this paper proposes a time series optimization-based method to calculate control parameters, which enables each DER to be independently controlled by an exclusive characteristic curve for optimizing its reactive power provision. To realize time series optimizations, the open-source tools pandapower and PowerModels are interconnected functionally. Based on the optimization results, Q(V)- and Q(P)-characteristic curves can be individually calculated using the linear decision tree regression to support voltage stability and provide reactive power flexibility and potentially reduce grid losses and component loadings. In this paper, the newly calculated characteristic curves are applied in two representative case studies, and the results demonstrate that the proposed method outperforms the reference ones suggested by grid codes.

Industrial data scarcity is one of the largest factors holding back the widespread use of machine learning in manufacturing. To overcome this problem, the concept of transfer learning was developed and it achieved high attention in recent industrial research. Our paper focuses on the problem of time series segmentation and presents the first in-depth research about transfer learning for deep-learning based time series segmentation on the example of industrial end-of-line pump testing. In particularly, we investigate if the performance of deep learning models can be increased by pretraining the network with data from other domains. Three different scenarios are analyzed: source and target data being closely related, source and target data being distantly related, and source and target data being non-related. The results demonstrate that transfer learning can enhance the performance of time series segmentation models in respect to accuracy and training speed. The benefit is most clearly seen in scenarios where source and training data are closely related and the number of target training data samples is lowest. However, in the scenario of non-related datasets, cases of negative Transfer Learning were observed as well. Thus, the research emphasizes the potential, but also the challenges of industrial Transfer Learning.

Vegetation status assessment is crucial for agricultural monitoring and management. Vegetation indices derived from high resolution image time series can be used to derive key phenological parameters for annual crops. In this work, we propose a procedure for the estimation of these parameters and their associated uncertainties. The approach uses Bayesian inference through Markov Chain Monte Carlo in order to obtain the full joint posterior distribution of the phenological parameters given the satellite observations. The proposed algorithm is quantitatively validated on synthetic data. Its use on real data is presented together with an application to real-time within season estimation allowing for phenology forecasting.