A Study on Time Series Forecasting Using ARIMA, LSTM, and GRU Models

Background: This study intends to identify the best model for predicting the incidence of hand, foot and mouth disease (HFMD) in Ningbo by comparing Autoregressive Integrated Moving Average (ARIMA) and Long Short-Term Memory Neural Network (LSTM) models combined and uncombined with exogenous meteorological variables. Methods: The data of daily HFMD incidence in Ningbo from January 2014 to November 2017 were set as the training set, and the data of December 2017 were set as the test set. ARIMA and LSTM models combined and uncombined with exogenous meteorological variables were adopted to fit the daily incidence of HFMD by using the data of the training set. The forecasting performances of the four fitted models were verified by using the data of the test set. Root mean square error (RMSE) was selected as the main measure to evaluate the performance of the models. Results: The RMSE for multivariate LSTM, univariate LSTM, ARIMA and ARIMAX (Autoregressive Integrated Moving Average Model with Exogenous Input Variables) was 10.78, 11.20, 12.43 and 14.73, respectively. The LSTM model with exogenous meteorological variables has the best performance among the four models and meteorological variables can increase the prediction accuracy of LSTM model. For the ARIMA model, exogenous meteorological variables did not increase the prediction accuracy but became the interference factor of the model. Conclusions: Multivariate LSTM is the best among the four models to fit the daily incidence of HFMD in Ningbo. It can provide a scientific method to build the HFMD early warning system and the methodology can also be applied to other communicable diseases.

China's garlic production accounts for more than 70% of the world's total output, and it is one of the most profitable agricultural products exported by China. Since 2003, garlic prices have fluctuated sharply and frequently, which has brought severe challenges to the healthy and sustainable development of China's garlic industry. Based on the analysis and comparison of various price prediction models, this paper constructs an EEMD-GRU combined prediction model. The model first uses the EEMD decomposition method to decompose the garlic price series on multiple time scales, and obtains 12 IMF eigenmode functions, which are classified and integrated to obtain high-frequency, intermediate and low-frequency terms. The analysis found that the low-frequency and intermediate-frequency items have a high contribution rate to the garlic price, and their contribution rates add up to 94%. Import the reconstructed garlic price sequence into the GRU model, select 50 training times and 30 hidden neurons to predict the garlic price, and obtain the prediction results. The prediction results obtained by the EEMD-GRU combined model are combined with ARIMA and ARIMA through evaluation indicators such as MSE. Comparing the prediction results obtained by ARIMA-SVR and LSTM models, it is found that the EEMD-GRU combined model has the highest trend prediction accuracy, the smallest prediction error, and the prediction effect is significantly better than the ARIMA, ARIMA-SVR and LSTM models. This research can help garlic-related industries to make a reasonable market allocation.

The increasing penetration of renewable energy, and wind power in particular, requires accurate short-term forecasting to ensure grid stability, reduce operational uncertainty, and facilitate large-scale integration of intermittent resources. This study evaluates Transformer-based architectures for wind power forecasting using hourly generation data from Spain (2020–2024). Time series were segmented into input windows of 12, 24, and 36 h, and multiple model configurations were systematically tested. For benchmarking, LSTM and GRU models were trained under identical protocols. The results show that the Transformer consistently outperformed recurrent baselines across all horizons. The best configuration, using a 36 h input sequence with moderate dimensionality and shallow depth, achieved an RMSE of 370.71 MW, MAE of 258.77 MW, and MAPE of 4.92%, reducing error by a significant margin compared to LSTM and GRU models, whose best performances reached RMSEs above 395 MW and MAPEs above 5.7%. Beyond predictive accuracy, attention maps revealed that the Transformer effectively captured short-term fluctuations while also attending to longer-range dependencies, offering a transparent mechanism for interpreting the contribution of historical information to forecasts. These findings demonstrate the superior performance of Transformer-based models in short-term wind power forecasting, underscoring their capacity to deliver more accurate and interpretable predictions that support the reliable integration of renewable energy into modern power systems.

Recurrent neural networks for complicated seismic dynamic response prediction of a slope system

Ambient air pollution affects human health, vegetative growth and sustainable socio-economic development. Therefore, air pollution data in Dezhou City in China are collected from January 2014 to December 2023, and multiple deep learning models are used to forecast air pollution PM2.5 concentrations. The ability of the multiple models is evaluated and compared with observed data using various statistical parameters. Although all eight deep learning models can accomplish PM2.5 forecasting assignments, the precision accuracy of the CNN-GRU-LSTM forecasting method is 34.28% higher than that of the ANN forecasting method. The result shows that CNN-GRU-LSTM has the best forecasting performance compared to the other seven models, achieving an R (correlation coefficient) of 0.9686 and an RMSE (root mean square error) of 4.6491 μg/m3. The RMSE values of CNN, GRU and LSTM models are 57.00%, 35.98% and 32.78% higher than that of the CNN-GRU-LSTM method, respectively. The forecasting results reveal that the CNN-GRU-LSTM predictor remarkably improves the performances of benchmark CNN, GRU and LSTM models in overall forecasting. This research method provides a new perspective for predictive forecasting of ambient air pollution PM2.5 concentrations. The research results of the predictive model provide a scientific basis for air pollution prevention and control.

The creation of a water quality monitoring by digital image analysis and developments in prawn farming and aquaculture in Kothapatnam, Ongole, Andhra Pradesh are both covered in this extensive research. In order to manage aquaculture in a sustainable and profitable manner, water quality prediction (WQP) is essential. This study presents new deep learning (DL) models for aquaculture WQP that combine CNN, LSTM, and GRU, and are specifically designed for this purpose. While GRU and LSTM are great at learning long-term relationships in time series data, CNNs are great at capturing the features of aquaculture water quality. By running trials on two separate water quality datasets, we were able to thoroughly examine how hyperparameters affected the performance of these hybrid DL models. The suggested CNN, LSTM & GRU hybrid models are tested against CNN, LSTM, and GRU models. In terms of computing speed and prediction accuracy, our research shows that the hybrid LSTM model is the best option for forecasting aquaculture water quality.

Cloud computing has become indispensable for meeting the rising demand for compute-intensive applications by providing cost-effective computational and storage resources. As reliance on cloud services increases, optimizing resource allocation is more critical than ever. This study introduces CloudProphet, an innovative machine learning-based framework designed to predict virtual machine (VM) performance in cloud environments. The approach begins with Dynamic Time Warping (DTW) to classify different types of applications based on their behavioral patterns. It further employs Pearson correlation to identify runtime metrics that are highly correlated with performance, ensuring that only the most relevant features are used in prediction models. These selected metrics are incorporated into three variations of deep learning models for evaluation: (1) an LSTM model without the use of DTW or feature selection, (2) an LSTM model with both DTW classification and selected features, and (3) a GRU model leveraging both DTW and highly correlated runtime indicators. Among these, the GRU-based approach demonstrates superior performance, achieving a remarkable 99.3% accuracy in predicting VM performance. The methodology is validated using a publicly available cloud workload dataset from GitHub and is further enhanced through real-time experimentation on live datasets to ensure practical applicability. The results highlight the robustness and accuracy of the proposed GRU model in forecasting both application types and VM behavior, making it a powerful tool for improving cloud resource management. By effectively anticipating workload demands and system performance, CloudProphet aids in reducing latency, minimizing resource wastage, and enhancing overall cloud service efficiency. This study underscores the value of combining time-series alignment techniques like DTW with correlation-based metric selection and advanced deep learning models such as GRU, ultimately offering a scalable and accurate solution for proactive and intelligent cloud performance prediction.

Near-field tides prediction for tsunami detection in the coastal area is a significant problem of the cable-based tsunami meter system in north Sipora, Indonesia. The problem is caused by its shallow water condition and the unavailability of an applicable model or research for tsunami detection in this area. The problem foundation of shallow water area is its ambient noise level-dependent property that requires preprocessing to improve its feature representation. Moreover, because this shallow water is close to the land area, we must consider a model that can accommodate low prediction time for a Tsunami Early Warning System. Therefore, we propose a recurrent neural network (RNN) model because of its reliable performance for time series forecasting. Our report evaluates variants of the RNN model (the vanilla RNN, LSTM and GRU models) in tides prediction and z-score analysis for tsunami identification. The GRU model overwhelms the other two variants in error scores and time processed (training and prediction). It can achieve median error score distribution of 7.8×10-5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$7.8 \ imes 10^{-5}$$\\end{document} on the L1000-P250 configuration with time prediction under 0.1 s. This lower-time prediction is necessary to ensure the early warning system is going well. Moreover, the GRU model can identify all synthetic tsunami tide spikes (compared with the ground truth result) from magnitude 7.2–8.2 by applying a z-score on the GRU’s prediction.

This study investigates air temperature forecasting in the city of Belém-PA, comparing the performance of the SARIMA and LSTM models. To this end, daily data from the ERA5-Land database was used and statistical metrics such as mean absolute error (MAE), mean squared error (MSE) and coefficient of determination (R²) were evaluated, supported by ANOVA, Shapiro-Wilk, Levene and Tukey tests. The results indicate that the LSTM model was more accurate, capturing complex patterns better than SARIMA. The findings reinforce the potential of recurrent neural networks in climate modeling and suggest new approaches for improving weather forecasting.

Joint overheating in low-voltage distribution cabinets presents a major safety risk, often leading to insulation failure, accelerated aging, and even fires. Conventional threshold-based inspection methods are limited in detecting early temperature evolution and lack predictive capabilities. To address this, a short-term temperature prediction method for electrical joints based on deep learning is proposed. Using a self-developed sensing device and Raspberry Pi edge nodes, multi-source data—including voltage, current, power, and temperature—were collected and preprocessed. Comparative experiments with ARIMA, GRU, and LSTM models demonstrate that the LSTM achieves the highest prediction accuracy, with an RMSE, MAE, and MAPE of 0.26 °C, 0.21 °C, and 0.54%, respectively. Furthermore, a lightweight version of the model was optimized for edge deployment, achieving a comparable accuracy (RMSE = 0.27 °C, MAE = 0.21 °C, MAPE = 0.67%) while reducing the inference latency and memory cost. The model effectively captures temperature fluctuations during 6 h prediction tasks and maintains stability under different cabinet scenarios. These results confirm that the proposed edge-enabled lightweight LSTM model achieves a balanced trade-off between accuracy, real-time performance, and efficiency, providing a feasible technical solution for intelligent temperature monitoring and predictive maintenance in low-voltage distribution systems.

In today's era of rapid economic growth, there is an increasing demand for workers to increase productivity by working longer and harder. However, these demands often lead to irregular and excessive working hours, which can potentially lead to negative consequences, such as physical fatigue-a state in which the body feels tired after physical activity. Factors that influence this fatigue include age, gender, health conditions, workload and work environment. Physical fatigue poses a significant challenge in ensuring workplace safety, especially in the transportation and industrial sectors, as it can reduce overall performance, productivity and quality of work. In addition, physical fatigue also increases the likelihood of decision-making errors and workplace accidents. Predicting physical fatigue is crucial to addressing these challenges. Heart rate serves as a parameter to measure fatigue, given its proven efficacy as a marker to predict physical fatigue, which is derived from the electrocardiogram and regulated by the autonomic nervous system. This research utilizes two machine learning algorithms - ARIMA and LSTM - with heart rate (bpm) and number of steps as variables. Performance evaluation, using Mean Squared Error (MSE) and Root Mean Squared Error (RMSE), showed that the LSTM model outperformed the ARIMA model. The LSTM model showed better performance, with MSE of 0.1108 and RMSE of 0.3329, compared to the ARIMA model with MSE of 0.2397 and RMSE of 0.4895.

Accurate and reliable short-term runoff prediction plays a pivotal role in water resource management, agriculture, and flood control, enabling decision-makers to implement timely and effective measures to enhance water use efficiency and minimize losses. To further enhance the accuracy of runoff prediction, this study proposes a FA-LSTM model that integrates the Firefly algorithm (FA) with the long short-term memory neural network (LSTM). The research focuses on historical daily runoff data from the Dahuangjiangkou and Wuzhou Hydrology Stations in the Xijiang River Basin. The FA-LSTM model is compared with RNN, LSTM, GRU, SVM, and RF models. The FA-LSTM model was used to carry out the generalization experiment in Qianjiang, Wuxuan, and Guigang hydrology stations. Additionally, the study analyzes the performance of the FA-LSTM model across different forecasting horizons (1–5 days). Four quantitative evaluation metrics—mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R2), and Kling–Gupta efficiency coefficient (KGE)—are utilized in the evaluation process. The results indicate that: (1) Compared to RNN, LSTM, GRU, SVM, and RF models, the FA-LSTM model exhibits the best prediction performance, with daily runoff prediction determination coefficients (R2) reaching as high as 0.966 and 0.971 at the Dahuangjiangkou and Wuzhou Stations, respectively, and the KGE is as high as 0.965 and 0.960, respectively. (2) FA-LSTM model was used to conduct generalization tests at Qianjiang, Wuxuan and Guigang hydrology stations, and its R2 and KGE are 0.96 or above, indicating that the model has good adaptability in different hydrology stations and strong robustness. (3) As the prediction period extends, the R2 and KGE of the FA-LSTM model show a decreasing trend, but the whole model still showed feasible forecasting ability. The FA-LSTM model introduced in this study presents an effective new approach for daily runoff prediction.

Accurate prediction of the number of charging piles in residential areas can help save on charging pile construction and operating costs. This study considers the limitations of the traditional charging pile ratio planning method and the advantages and disadvantages of various single prediction methods across different aspects. In this paper, the number of charging piles in residential areas of Hangzhou is used as the raw data, and the linear time series features in the charging pile number data are captured by the autoregressive integrated moving average (ARIMA) model, and then the long shortterm memory (LSTM) model is used to learn the complex nonlinear time series features in the residual sequence. We established a combined prediction model for the number of charging piles in residential areas using both ARIMA and LSTM. The RMSE and MAPE were employed as the model's evaluation metrics. By comparing with the single ARIMA, LSTM, GRU, ETS, and ARIMA-GRU models, the proposed method has high accuracy (RMSE=2.13, MAPE=2.01%), and the MAPE is reduced by about 70% for different data series. In comparison to the combined model ARIMA-GRU, it is also reduced by nearly 12%.

To solve the active control of the shield vertical attitude, this paper established the GRU model to realize the prediction of the pitch angle, which can reflect the shield vertical attitude. Firstly, the tunneling parameters, geological parameters and geometric parameters were selected as the influencing factors sets, and a series of data pre-processing strategies were established. And then, the GRU model was established, mainly including the division of training data, the optimization of hyperparameters, the determination of the objective function and optimization algorithm. Eventually, the shield interval from Chengdu was used to verify the new model. As a result, compared with the BP model and LSTM model, it could be found that the MGRU model had higher accuracy. This study could provide references for the prediction and help the engineers to realize the active control in the field of the shield attitude.

The identification of braking intention is crucial for enhancing driver assistance features, enhancing braking safety, and maximizing energy recovery efficiency of electric vehicles. To accurately identify braking intention, a novel identification model utilizing an extreme learning machine (ELM) and optimized by the crayfish optimization algorithm (COA) is proposed. Based on extensive braking test data, data processing, model training, and verification are conducted. The initial braking data are denoised using variational mode decomposition (VMD) and Shannon entropy, and the Gaussian mixture model (GMM) is employed to label the braking intention. The brake pedal opening, its change rate, and vehicle speed serve as inputs for the ELM model, with the braking intention label as the output. The COA is utilized to optimize the hidden layer parameters of ELM, thereby enhancing the precision of the intention identification model. The results indicate that, compared with the LSTM model, GRU model and ELM model, the accuracy of the COA-ELM model improves by 2.73%, 1.56%, and 0.39% respectively, with identification accuracy reaching over 99.02%. This offers a reliable modeling basis for the development of subsequent braking strategies.