Time Series Models Research Articles

An anomaly detection model for multivariate time series with anomaly perception

Multivariate time series anomaly detection is a crucial data mining technique with a wide range of applications in areas such as IT applications. Currently, the majority of anomaly detection methods for time series data rely on unsupervised approaches due to the rarity of anomaly labels. However, in real-world scenarios, obtaining a limited number of anomaly labels is feasible and affordable. Effective usage of these labels can offer valuable insights into the temporal characteristics of anomalies and play a pivotal role in guiding anomaly detection efforts. To improve the performance of multivariate time series anomaly detection, we proposed a novel deep learning model named EDD (Encoder-Decoder-Discriminator) that leverages limited anomaly samples. The EDD model innovatively integrates a graph attention network with long short term memory (LSTM) to extract spatial and temporal features from multivariate time series data. This integrated approach enables the model to capture complex patterns and dependencies within the data. Additionally, the model skillfully maps series data into a latent space, utilizing a carefully crafted loss function to cluster normal data tightly in the latent space while dispersing abnormal data randomly. This innovative design results in distinct probability distributions for normal and abnormal data in the latent space, enabling precise identification of anomalous data. To evaluate the performance of our EDD model, we conducted extensive experimental validation across three diverse datasets. The results demonstrate the significant superiority of our model in multivariate time series anomaly detection. Specifically, the average F1-Score of our model outperformed the second-best method by 2.7% and 73.4% in both evaluation approaches, respectively, highlighting its superior detection capabilities. These findings validate the effectiveness of our proposed EDD model in leveraging limited anomaly samples for accurate and robust anomaly detection in multivariate time series data.

Time series modeling of coastal fishery landings on the Southwestern Atlantic shelf: Influence of environmental drivers

AbstractTime‐series modeling of fisheries provides insights into stock tendencies and enables short‐term forecasting of landings, aiding decision makers in establishing management priorities. The Rio de la Plata Estuary and its maritime front sustain valuable fisheries for Argentina and Uruguay, with striped weakfish (Cynoscion guatucupa), whitemouth croaker (Micropogonias furnieri), and Argentine hake (Merluccius hubbsi) historically representing highest catches. However, their landings have declined in recent decades. To support resource management, we investigated the effectiveness of Autoregressive Integrated Moving Average (ARIMA) models in capturing fishery landing dynamics and providing reliable short‐term predictions. The best models exhibited a good fit and accurately captured the overall trends of landings. Residual variability unaccounted for by the model was analyzed in relation to time‐lagged environmental conditions. A wavelet coherence analysis was employed to examine the effect of the most significant variables on landings. Results revealed that environmental conditions affect differentially landings of each species as a result of their particular ecological traits. Turbidity and salinity affected mainly M. furnieri, which inhabits the innermost part of the estuary. Additionally, C. guatucupa, inhabiting the outer estuary and coastal region, exhibited a stronger association with river runoff compared to M. hubbsi, which inhabits the continental shelf. This study provides the first evidence of ARIMA models' reliability in representing the temporal evolution of catch in these fisheries, offering valuable tools for short‐term landings forecasting and facilitating sustainable management. Wavelet analysis findings will also contribute to enhancing our comprehension of trends in the correlation between environmental conditions and commercial landings.

Lifting COVID-19-associated non-pharmaceutical interventions: potential impact on notifications of infectious diseases transmitted from person to person in 2022 in Bavaria, Germany

BackgroundThe COVID-19 pandemic and associated non-pharmaceutical interventions (NPIs) have led to substantial decreases in case numbers of infectious diseases in several countries worldwide. As NPIs were gradually lifted, intense or out-of-season outbreaks of respiratory and gastrointestinal diseases were reported, raising the hypothesis of a potential catch-up effect of infections. By analysing surveillance data from the federal reporting system for notifiable infectious diseases, we aimed to assess the potential impact of lifting COVID-19 associated NPIs on notifications of selected infectious diseases in Bavaria, 2022.MethodsWe compared influenza, chickenpox, norovirus gastroenteritis, rotavirus gastroenteritis weekly case numbers in a pre-pandemic period (2016–2019) and 2022 using two time series analyses approaches: (i) a predictive model forecasting weekly case numbers for the pandemic years 2020–2022, based on 2016–2019 data, (ii) interrupted time series model, based on 2016–2022 data, including a term per pandemic period.ResultsIn 2022, incidence rates were higher compared to pre-pandemic period for influenza (IRR = 3.47, 95%CI: 1.49–7.94) and rotavirus gastroenteritis (IRR = 1.36, 95%CI: 0.95–1.93), though not significant for rotavirus gastroenteritis. Conversely, case numbers remained significantly below pre-pandemic levels for chickenpox (IRR = 0.52, 95%CI: 0.41–0.65) and norovirus gastroenteritis (IRR = 0.59, 95%CI: 0.42–0.82). Seasonality changed notably for influenza, showing an earlier influenza wave compared to pre-pandemic periods.ConclusionThe lifting of NPIs was associated with heterogenic epidemiological patterns depending on the selected disease. The full impact of NPIs and their discontinuation may only become clear with continued monitoring and assessment of potential additional contributing factors.

Estimation of Lithium Battery State of Charge Using the LTG-SABO-GRU Model

Abstract Accurate estimation of the state of charge (SOC) in lithium batteries is crucial for optimizing energy utilization and ensuring battery safety within Battery Management Systems (BMS). While deep learning techniques have made significant progress, time-series models based on the Gate Recurrent Unit (GRU) have gained widespread application in SOC estimation. However, their performance heavily hinges on the initial hyperparameter settings, impacting both precision and application range. To address this challenge, we propose a novel algorithm—the Logistic-tent-Gold Subtraction Average-based Optimizer (LTG-SABO)—which combines composite chaotic mapping with the golden sine algorithm. The LTG-SABO algorithm aims to optimize key hyperparameters of the GRU model, thereby enhancing precision and robustness in SOC estimation. By leveraging the Logistic-tent composite chaotic mapping for population initialization, our approach not only expands the search space but also effectively prevents algorithm convergence to local optima. Additionally, integrating the Gold-SA strategy further enhances the global search capability of the SABO algorithm, significantly reducing convergence time. The computational results reveal that the proposed LTG-SABO-GRU model outperforms the traditional GRU model in estimating SOC precision under both normal and extreme temperature conditions. Specifically, the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) show a substantial improvement, increasing by over 50% compared to the traditional model. Moreover, the LTG-SABO-GRU model exhibits significantly fewer convergence iterations than existing typical population optimization algorithms. This study introduces a novel, efficient, and practical approach for SOC estimation in BMS applications.

Exploring the Depths of the Autocorrelation Function: Its Departure from Normality

In this article, we study the autocorrelation function (ACF), which is a crucial element in time series analysis. We compare the distribution of the ACF, both from a theoretical and empirical point of view. We focus on white noise processes (WN), i.e., uncorrelated, centered, and identically distributed variables, whose ACFs are supposed to be asymptotically independent and converge towards the same normal distribution. But, the study of the sum of the sample ACF contradicts this property. Thus, our findings reveal a deviation of the sample ACF from normality beyond a specific lag. Note that this phenomenon is observed for white noise of varying lengths, and evenforn the residuals of an ARMA(p,q) model. This discovery challenges traditional assumptions of normality in time series modeling. Indeed, when modeling a time series, the crucial step is to validate the estimated model by checking that the associated residuals form white noise. In this study, we show that the widely used portmanteau tests are not completely accurate. Box–Pierce appears to be too conservative, whereas Ljung–Box is too liberal. We suggest an alternative method based on the ACF for establishing the reliability of the portmanteau test and the validity of the estimated model. We illustrate our methodology using money stock data in the USA.

End-to-End Modeling and Long Short-Term Memory Application in Time Series Modeling

With the vigorous development of e-commerce, accurately modeling and predicting user behavior has become a key factor in improving business efficiency. Precisely understanding user behavior not only enables companies to provide personalized services but also allows them to stand out in the intense market competition. This study aims to explore the effectiveness of applying end-to-end models, Long Short-Term Memory (LSTM), and attention mechanisms in time series modeling to enhance the performance of modeling and predicting user behavior in e-commerce. In the methodology section, we first introduce the basic principles of the end-to-end model, which extracts features directly from raw data for prediction, avoiding the need for intricate feature engineering. Simultaneously, we introduce Long Short-Term Memory (LSTM) to better capture long-term dependencies in time series data.

Settlement estimation during foundation excavation using pattern analysis and explainable AI modeling

With the rapid expansion of underground engineering, accurate settlement estimation during foundation excavation using monitoring data has gained prominence. Previous studies have typically overlooked data patterns, relying solely on time-series models, which yielded limited accuracy and short-term predictability. To address these issues, this paper performs a thorough pattern analysis covering both the temporal and spatial properties, and proposes a spatiotemporal modeling method grounded in explainable artificial intelligence technique. A real-world engineering case study is conducted to validate the effectiveness of the proposed method. Counterintuitively, the results reveal a weak temporal effect within the settlement data, with only the last step playing a dominant role, whereas the spatial correlation among measuring points is notably more significant. Compared to conventional models, the proposed method consistently outperforms, achieving significantly higher R2 scores and excelling in long-term estimation with reductions of at least 78% in RMSE, 80% in MAE, and 72% in MAPE.

Handling Volatility and Nonlinearity in Wind Speed Data: A Comparative Analysis between ARIMA-GARCH and ARIMA-MLP

One of the notable features of wind speed is its volatility and nonlinearity. Thorough assessment on the presence of these features is crucial to obtain a wind speed forecasting model with higher accuracy. In this study, the conventional time series linear model; ARIMA model was applied to assess the internal structure of the wind speed daily data in two stations in Johor; Senai and Mersing. Due to the existence of some nonlinearity features in the residuals part of ARIMA modelling, two nonlinear models were introduced to capture the internal structure of the residual data. Both conventional time series models; GARCH, and machine learning model; MLP was applied to model the residuals of ARIMA model. The out-sample performance in forecasting accuracy was compared between the ARIMA-GARCH model and the ARIMA-MLP model. The findings proves that MLP model has outperformed GARCH model in capturing the dynamics in the residual data by providing the lowest error measurements. Thus, the machine learning approaches has proven its superiority against the conventional time series nonlinear model in handling the nonlinearity in the daily wind speed series for wind speed forecasting.

Computer-aided prognosis of tuberculous meningitis combining imaging and non-imaging data

Tuberculous meningitis (TBM) is the most lethal form of tuberculosis. Clinical features, such as coma, can predict death, but they are insufficient for the accurate prognosis of other outcomes, especially when impacted by co-morbidities such as HIV infection. Brain magnetic resonance imaging (MRI) characterises the extent and severity of disease and may enable more accurate prediction of complications and poor outcomes. We analysed clinical and brain MRI data from a prospective longitudinal study of 216 adults with TBM; 73 (34%) were HIV-positive, a factor highly correlated with mortality. We implemented an end-to-end framework to model clinical and imaging features to predict disease progression. Our model used state-of-the-art machine learning models for automatic imaging feature encoding, and time-series models for forecasting, to predict TBM progression. The proposed approach is designed to be robust to missing data via a novel tailored model optimisation framework. Our model achieved a 60% balanced accuracy in predicting the prognosis of TBM patients over the six different classes. HIV status did not alter the performance of the models. Furthermore, our approach identified brain morphological lesions caused by TBM in both HIV and non-HIV-infected, associating lesions to the disease staging with an overall accuracy of 96%. These results suggest that the lesions caused by TBM are analogous in both populations, regardless of the severity of the disease. Lastly, our models correctly identified changes in disease symptomatology and severity in 80% of the cases. Our approach is the first attempt at predicting the prognosis of TBM by combining imaging and clinical data, via a machine learning model. The approach has the potential to accurately predict disease progression and enable timely clinical intervention.

Predicting the epidemiological trend of acute hemorrhagic conjunctivitis in China using Bayesian structural time-series model

This study aims to explore the application value of the Bayesian Time Structure Sequence (BSTS) model in estimating the acute hemorrhagic conjunctivitis (AHC) epidemics. The reported AHC cases spanning from January 2011 to October 2022 in China were collated. Utilizing R software, the BSTS and Autoregressive Integrated Moving Average (ARIMA) models were constructed using the data from January 2011 to December 2021. The prediction effect of both models was compared using the data from January to October 2022, and finally the AHC incidence from November 2022 to December 2023 was predicted. The results indicated that forecast errors under the BSTS model were lower than those under the ARIMA model. The actual AHC incidence in July 2022 from the ARIMA model deviated from the 95% confidence interval (CI) of the predicted value. However, the observed AHC incidence from the BSTS model fell within the 95% CI of the predicted value. Notably, the BSTS model predicted 26,474 new AHC cases in China from November 2022 to December 2023, exhibiting better prediction performance compared to the ARIMA model. This indicates that the BSTS model possesses a high application value for forecasting the epidemic trends of AHC, making it a valuable tool for disease surveillance and prevention strategies.

General estimation results for tdVARMA array models

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

Influence of population mobility on electricity consumption in seven U.S. cities during the COVID-19 pandemic

We examine the impact of the COVID-19 pandemic on electricity consumption in seven U.S. cities. A high-level analysis reveals that reductions in electricity consumption were mostly short-term, mainly when lockdowns were first introduced. Bayesian structural time series modeling was used to decompose electricity consumption into multiple tailored components to better understand the pandemic's impact. We find that models incorporating population mobility achieved high accuracy rates using pre-pandemic data and even better rates using post-pandemic data. Electricity usage dropped during the first six weeks of the pandemic in all but one of the cities studied.

Linear and nonlinear time-series methodologies for bridge condition assessment: A literature review

Railway bridges are essential components of any transportation system and are typically subjected to several environmental and operational actions that can cause damage. Furthermore, they are not easily replaced, and their failure can have catastrophic consequences. Considering the expected lifespan of bridges, it is essential to guarantee their adequate serviceability and safety. In this scenario, emerges the Structural Health Monitoring (SHM), which allows the early identification of damage before it becomes critical. Damage identification is usually performed by the comparison between the damaged and undamaged responses obtained from monitoring data. Among the several features extracted from the responses, the time-series models exhibit a better performance, capability of early damage detection, and may also be applied within online damage detection strategies using unsupervised machine learning frameworks. In this paper, a review of advanced time-series methodologies for damage detection is presented. Initially, several time-series models often used in SHM are described, such as Autoregressive Models (AR), Recurrent Neural Networks (RNN), Gated Recurrent Unit (GRU), and Long Short-Term Memory (LSTM). Later, the framework where these models are usually applied is also detailed, including the latest upgrades and most relevant results. Finally, the conclusions summarize and elucidate the current perspectives and research gaps on the time-series models.

Improved time series models for the prediction of lane-change intention

ABSTRACT To improve the accuracy of lane-change intention prediction and analyze the influence of driving styles on prediction outcomes, the T-Encoder-Sequence model is proposed in this paper. It integrates the Transformer’s encoder module with various recurrent neural network (RNN) models and introduces a multimodal fusion input structure. Building on this, a risk indicator model, capable of reflecting driver stress, is established to calculate the model’s input parameters. Consequently, the model can simultaneously capture global information and consider the impact of vehicle classes on drivers. Furthermore, the k-means++ algorithm is employed to categorize vehicle trajectories into conservative, conventional, and aggressive types for further analysis. The results demonstrate that training the model with risk indicator parameters markedly enhances prediction performance. Under identical input parameters, the T-Encoder-Sequence model exhibits notably superior prediction efficacy compared to the original model. The T-Encoder-Sequence model, trained with risk indicator parameters, demonstrates substantial advantages compared to other studies.

Marginal inference for hierarchical generalized linear mixed models with patterned covariance matrices using the Laplace approximation

AbstractWe develop hierarchical models and methods in a fully parametric approach to generalized linear mixed models for any patterned covariance matrix. The Laplace approximation is used to marginally estimate covariance parameters by integrating over all fixed and latent random effects. The Laplace approximation relies on Newton–Raphson updates, which also leads to predictions for the latent random effects. We develop methodology for complete marginal inference, from estimating covariance parameters and fixed effects to making predictions for unobserved data. The marginal likelihood is developed for six distributions that are often used for binary, count, and positive continuous data, and our framework is easily extended to other distributions. We compare our methods to fully Bayesian methods, automatic differentiation, and integrated nested Laplace approximations (INLA) for bias, mean‐squared (prediction) error, and interval coverage, and all methods yield very similar results. However, our methods are much faster than Bayesian methods, and more general than INLA. Examples with binary and proportional data, count data, and positive‐continuous data are used to illustrate all six distributions with a variety of patterned covariance structures that include spatial models (both geostatistical and areal models), time series models, and mixtures with typical random intercepts based on grouping.

Detection of Individual Corn Crop and Canopy Delineation from Unmanned Aerial Vehicle Imagery

Precise monitoring of individual crop growth and health status is crucial for precision agriculture practices. However, traditional inspection methods are time-consuming, labor-intensive, prone to human error, and may not provide the comprehensive coverage required for the detailed analysis of crop variability across an entire field. This research addresses the need for efficient and high-resolution crop monitoring by leveraging Unmanned Aerial Vehicle (UAV) imagery and advanced computational techniques. The primary goal was to develop a methodology for the precise identification, extraction, and monitoring of individual corn crops throughout their growth cycle. This involved integrating UAV-derived data with image processing, computational geometry, and machine learning techniques. Bi-weekly UAV imagery was captured at altitudes of 40 m and 70 m from 30 April to 11 August, covering the entire growth cycle of the corn crop from planting to harvest. A time-series Canopy Height Model (CHM) was generated by analyzing the differences between the Digital Terrain Model (DTM) and the Digital Surface Model (DSM) derived from the UAV data. To ensure the accuracy of the elevation data, the DSM was validated against Ground Control Points (GCPs), adhering to standard practices in remote sensing data verification. Local spatial analysis and image processing techniques were employed to determine the local maximum height of each crop. Subsequently, a Voronoi data model was developed to delineate individual crop canopies, successfully identifying 13,000 out of 13,050 corn crops in the study area. To enhance accuracy in canopy size delineation, vegetation indices were incorporated into the Voronoi model segmentation, refining the initial canopy area estimates by eliminating interference from soil and shadows. The proposed methodology enables the precise estimation and monitoring of crop canopy size, height, biomass reduction, lodging, and stunted growth over time by incorporating advanced image processing techniques and integrating metrics for quantitative assessment of fields. Additionally, machine learning models were employed to determine relationships between the canopy sizes, crop height, and normalized difference vegetation index, with Polynomial Regression recording an R-squared of 11% compared to other models. This work contributes to the scientific community by demonstrating the potential of integrating UAV technology, computational geometry, and machine learning for accurate and efficient crop monitoring at the individual plant level.

MODEL PERAMALAN PERGERAKAN PENUMPANG DOMESTIK DI BANDAR UDARA YOGYAKARTA INTERNATIONAL AIRPORT

This research is quantitative descriptive research which aims to make predictions using the ARIMA model time series forecasting method. The data obtained was analyzed using the R program. The data used for forecasting is the number of arrivals and departures of domestic passengers at Yogyakarta International Airport for the period January 2022 – December 2023. Based on the results of data analysis, it is known that the ARIMA model time series forecasting method is the best for predicting the number of arrivals. and domestic passenger departures at Yogyakarta International Airport are the AR (1,0,0) model. This method was chosen because the results were significant, met the white noise requirements and had the smallest MAPE value.

Modeling Nairobi Residential Real Estate Prices using ARIMA

The residential real estate market is big and affords investors investment opportunities. The price changes are key in determining the overall return. Structural and atheoretical models are the two main approaches to modeling real estate prices. Structural models link prices to fundamental factors such as economic indicators and property supply, amongst others. Atheoretical models attempt to predict prices by leveraging on the statistical properties of time series data and may be extended to augment fundamental factors. This study focused on time series modeling using ARIMA. The objective of the paper was to identify a suitable ARIMA model that is efficient in predicting house prices in Nairobi. The training data was for the period 2010Q3 to 2019Q2. The out of sample test data was for six quarters: 2019Q3 to 2020Q4. The Box-Jenkins methodology was adopted. Seven ARIMA models and six AR models were identified, estimated, and used in predicting prices using out of sample data. The study found out that AR models outperformed ARIMA models. The paper contributes to knowledge being among the first to apply ARIMA in Nairobi house market using hedonic house prices. The paper may inform investment strategy and portfolio management by investors. It may inform policy since house price forecasts may have social and economic effects.

Research on Optimization of Rural Financial Policies Based on Econometrics

Rural finance is vital for rural economic development. This study uses extensive empirical data and econometric models to analyze factors influencing rural finance development in China. It employs multiple linear regression, panel data, and time series models, optimizing them through feature selection, non-linear processing, and cross-validation. Scenarios such as baseline, fiscal support, interest rate preferences, and inclusive finance are simulated to assess impacts on rural loan balances and resident income levels. The findings highlight that comprehensive measures yield better policy synergies, offering policy optimization suggestions for decision-makers.

Transformer models for astrophysical time series and the GRB prompt-afterglow relation

Transformer models for astrophysical time series and the GRB prompt-afterglow relation