A temporal fusion transformer for multi-step forecasting of Indonesia’s strategic food commodity prices

The increasing use of cryptocurrencies has changed the dynamics of investment, presenting both opportunities and challenges for investors. Although various studies have compared the performance of Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) in predicting financial asset prices, there are still differences in results regarding which model is superior. Therefore, this study aims to compare the performance of LSTM and GRU in predicting Ethereum prices using a hyperparameter tuning approach. The data used is historical data of Ethereum (ETH) shares from 2020 to 2025. The research methodology includes data preprocessing using Min-Max scaling, model development with various layer configurations, and comprehensive evaluation using several performance metrics. The results show that the GRU Model provides superior performance with a lower Root Mean Squared Error (RMSE) of 0.0234 and Mean Absolute Error (MAE) of 0.0168, compared to LSTM's RMSE of 0.0265 and MAE of 0.0193. While LSTM exhibits a slightly better Mean Absolute Percentage Error (MAPE) of 18.08% compared to GRU at 18.17%, the GRU model achieves a higher R² Score of 0.9442 compared to LSTM at 0.9282. Visual analysis of the prediction patterns and residual distributions further demonstrates GRU’s more consistent and accurate performance in capturing Ethereum price movements. These findings suggest that while both models are effective for cryptocurrency price prediction, GRU offers slightly better overall performance and stability, especially in maintaining consistent prediction accuracy across different market conditions.

Cryptocurrency represents a form of asset that has arisen from the progress of financial technology, presenting significant prospects for scholarly investigations. The ability to anticipate cryptocurrency prices with extreme accuracy is very desirable to researchers and investors. However, time-series data presents significant challenges due to the nonlinear nature of the cryptocurrency market, complicating precise price predictions. Several studies have explored cryptocurrency price prediction using various deep learning (DL) algorithms. Three leading cryptocurrencies, determined by market capitalization, Ethereum (ETH), Bitcoin (BTC), and Litecoin (LTC), are examined for exchange rate predictions in this study. Two categories of recurrent neural networks (RNNs), specifically long short-term memory (LSTM) and gated recurrent unit (GRU), are employed. Four performance metrics are selected to evaluate the prediction accuracy namely mean squared error (MSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean squared error (RMSE) for three cryptocurrencies which demonstrates that GRU model outperforms LSTM. The GRU model was implemented as a two-layer deep learning network, optimized using the Adam optimizer with a dropout rate of 0.2 to prevent overfitting. The model was trained using normalized historical price data sourced from CryptoDataDownload, with an 80:20 train-test split. In this work, GRU qualifies as the best algorithm for developing a cryptocurrency price prediction model. MAPE values for BTC, LTC and ETH are 0.03540, 0.08703 and 0.04415, respectively, which indicate that GRU offers the most accurate forecasts as compared to LSTM. These prediction models are valuable for traders and investors, offering accurate cryptocurrency price predictions. Future studies should also consider additional variables, such as social media trends and trade volumes that may impact cryptocurrency pricing.

Accurate forecasting of agricultural commodity prices is essential for market planning and policy formulation, especially in agriculture-dependent economies like India. Price volatility, driven by factors such as weather variability and market demand fluctuations, poses significant forecasting challenges. This study evaluates the performance of traditional stochastic models, machine learning techniques, and deep learning approaches in forecasting the prices of 23 commodities using daily wholesale price data from January 2010 to June 2024. Models assessed include Autoregressive Integrated Moving Average, Support Vector Regression, Extreme Gradient Boosting, Multilayer Perceptron, Recurrent Neural Networks, Long Short-Term Memory Networks, Gated Recurrent Units, and Echo State Networks. Results show that deep learning models, particularly Long Short-Term Memory and Gated Recurrent Units, outperform others in capturing complex temporal patterns, achieving superior accuracy across error metrics. The results indicate that deep learning models, particularly Long Short-Term Memory (LSTM) networks and Gated Recurrent Units (GRU), demonstrate superior performance in capturing complex temporal patterns. For instance, the GRU model achieved a Root Mean Squared Error (RMSE) of 369.54 for onions and 210.35 for tomatoes, significantly outperforming the ARIMA model, which recorded RMSE values of 1564.62 and 1298.60, respectively. Furthermore, the Mean Absolute Percentage Error (MAPE) for GRU was notably lower, at 14.59% for onions and 10.58% for tomatoes. These results underscore the efficacy of deep learning approaches in addressing the inherent volatility and nonlinear dynamics of agricultural commodity prices. These findings offer valuable insights for policymakers, traders, and farmers, enabling better market interventions, crop planning, and risk management. The study recommends exploring hybrid models and incorporating external factors like weather data to further enhance forecasting reliability.

Prediction of dissolved oxygen in a fishery pond based on gated recurrent unit (GRU)

The work presented in this paper aims to improve the accuracy of forecasting models in univariate time series, for this it is experimented with different hybrid models of two and four layers based on recurrent neural networks such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU). It is experimented with two time series corresponding to downward thermal infrared and all sky insolation incident on a horizontal surface obtained from NASA’s repository. In the first time series, the results achieved by the two-layer hybrid models (LSTM + GRU and GRU + LSTM) outperformed the results achieved by the non-hybrid models (LSTM + LSTM and GRU + GRU); while only two of six four-layer hybrid models (GRU + LSTM + GRU + LSTM and LSTM + LSTM + GRU + GRU) outperformed non-hybrid models (LSTM + LSTM + LSTM + LSTM and GRU + GRU + GRU + GRU). In the second time series, only one model (LSTM + GRU) of two hybrid models outperformed the two non-hybrid models (LSTM + LSTM and GRU + GRU); while the four-layer hybrid models, none could exceed the results of the non-hybrid models.

Forecasting multistep daily stock prices for long-term investment decisions: A study of deep learning models on global indices

The aim of this study is to compare the performance of various deep learning models in predicting the arrival and charging time of an electric vehicle at a charging station. The objective is to identify the most precise model capable of predicting the time from the driver’s location to the arrival at the charging station. Initially, an effort was made to ascertain which model type offers superior prediction accuracy, characterized by low error rates and high success scores. To this end, the study examined the prediction capabilities of the LSTM (Long Short-Term Memory), GRU (Gated Recurrent Unit), Prophet, and ARIMA (Autoregressive Integrated Moving Average) models, which were trained with historical data using various metrics. These metrics included the R2 (R-squared)success metric, MAE (Mean Absolute Error) and MSE (Mean Squared Error) error metrics, DTW (Dynamic Time Warping) metric scores, and model selection. In MAE metric scores, GRU has an error rate of 0.38, LSTM 0.50, Prophet 0.61, and ARIMA 2.31. For MSE metric scores, GRU has an error rate of 2.92, LSTM 3.05, Prophet 4.21, and ARIMA 65.54. In R2 metric scores, GRU has a success rate of 0.99, LSTM 0.99, Prophet 0.13, and ARIMA −2.19. In DTW metric scores, GRU has a distance ratio of 125.5, LSTM 126.9, Prophet 185.9, and ARIMA 454.9. Based on these score values, it was decided that the GRU model made the most accurate time estimation. After observing the superior performance of the GRU model, the time prediction capability of this model is demonstrated through an interface program for charging stations in the province of Kocaeli, which serves as the model’s real-world application area. The main contribution of this article is that LSTM, GRU, Prophet, and ARIMA deep learning approaches, which are preferred in many studies, are used for the first time in the process of estimating electric vehicle charging time.

This paper presents a comparative analysis between Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) models for predicting cycling performance based on heart rate data. Heart rate is a key physiological parameter reflecting an athlete's effort, making it an effective predictor of lap completion time in endurance sports such as cycling. The study used time-series heart rate data collected from cycling sessions, processed in Google Colab using TensorFlow. The models were trained and evaluated using five performance metrics: Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Rsquared (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{R}^{\mathbf{2}}$</tex>), and Mean Absolute Percentage Error (MAPE). Results indicate that both LSTM and GRU models achieved high prediction accuracy, with LSTM yielding an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{R}^{\mathbf{2}}$</tex> of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{0. 9 3 9 8}$</tex> and GRU achieving an even higher <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{R}^{\mathbf{2}}$</tex> of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{0. 9 5 2 9}$</tex>. GRU also produced lower MAE and RMSE values, indicating more accurate and consistent predictions. The findings suggest that GRU is more efficient and suitable for heart rate-based performance forecasting in cycling, especially under limited data conditions. This study highlights the applicability of deep learning models for real-time sports analytics and supports further integration of GRU-based systems into personalized training and monitoring platforms.

This study presents a novel, integrated deep-learning framework named 2LE-BO-DeepTrade for stock closing price prediction. This framework combines 2LE-ICEEMDAN denoising, deep learning models tuned with Bayesian optimization, and a piecewise linear representation (PLR)-based trading strategy. The framework utilizes the model that provides the highest accuracy among optimized long short-term memory (LSTM), long short term memory with batch normalization (LSTM-BN), and gated recurrent unit (GRU) models on data preprocessed with the 2LE-ICEEMDAN denoising method. The model’s performance is comprehensively evaluated using both statistical metrics and a PLR-based trading strategy specifically developed for this study. Experimental studies were conducted on AKBNK, MGROS, KCHOL, THYAO, and ULKER stocks, which are traded on Borsa Istanbul and represent different sectors. During the denoising phase, noise in the stock prices was successfully removed, and noiseless intrinsic mode functions (IMFs) were obtained. The optimal model and hyperparameters for each IMF component were determined using Bayesian optimization, significantly improving prediction accuracy. The model within this framework, characterized by its optimized yet simple structure, demonstrated superior predictive performance compared to the more complex ICE2DE-MDL model in the literature. When compared to ICE2DE-MDL, the 2LE-BO-DeepTrade model, across all tested stocks, reduced the average root mean square error (RMSE) value by 94.4%, the average mean absolute error (MAE) value by 93.6%, and the average mean absolute percentage error (MAPE) value by 37.4% while increasing the average R2 value by 1.1%. Furthermore, the PLR-based trading strategy, specifically developed for this study, generated “Buy” and “Sell” signals, exhibiting a remarkably superior financial performance to a passive investment strategy. Across all considered stocks, the PLR-based strategy yielded, on average, 66 times more profit than the passive approach. These findings substantiate that the proposed integrated deep learning-based stock forecasting framework can significantly enhance the accuracy of stock market predictions and the returns of trading strategies.

Objectives : Photovoltaic power generation which significantly depends on meteorological conditions is intermittent and unstable. Therefore, accurate forecasting of photovoltaic power generation is a challenging task. In this research, random forest (RF), recurrent neural network (RNN), long short term memory (LSTM), and gated recurrent unit (GRU) are proposed and we will find an efficient model for forecasting photovoltaic power generation of photovoltaic power plants.Methods : We used photovoltaic power generation data from photovoltaic power plants at Gamcheonhang-ro, Saha-gu, Busan, and meteorological data from Busan Regional Meteorological Administration. We used solar irradiance, temperature, atmospheric pressure, humidity, wind speed, wind direction, duration of sunshine, and cloud amount as input variables. By applying the trial and error method, we optimized hyperparameters such as estimators in RF, and number of hidden layers, number of nodes, epochs, and validation split in RNN, LSTM, and GRU. We compared proposed models by evaluation indexes such as coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE).Results and Discussion : The best RF at 1,000 of number of decision tree achieved test R2=0.865, test RMSE=16.013, and test MAE=9.656. The best choice of RNN was 6 hidden layers and the number of nodes in each layer was 90. We set the epochs at 450. RNN achieved test R2=0.942, test RMSE=10.530, and test MAE=6.390. To find the best result of LSTM, we used 3 hidden layers, and the number of nodes was 600. The epochs were set to 200. LSTM achieved test R2=0.944, test RMSE=10.29, and test MAE=6.360. GRU was set to 3 hidden layer and the number of nodes was 450. The epochs were set to 500. GRU achieved test R2=0.945, test RMSE=10.189, and test MAE=5.968.Conclusions : We found RNN, LSTM, and GRU performed better than RF, and GRU model showed the best performance. Therefore, GRU is the most efficient model to predict photovoltaic power generation in Busan, Korea.

Predicting future prices of cryptocurrencies, including Bitcoin and Ethereum, presents a formidable challenge owing to their inherent volatility. This study applies Long Short-Term Memory (LSTM), a well-established recurrent neural network for time series forecasting, to predict Bitcoin and Ethereum values. Historical price data for both cryptocurrencies, sourced from Yahoo Finance, serves as the basis for analysis. The dataset undergoes an 80% training and 20% testing partition. Subsequently, LSTM models are developed and trained on both datasets. In parallel, the gated recurrent unit (GRU), recognized as an advanced variant of the LSTM model, is explored for comparative purposes. Performance evaluation utilizes fundamental metrics, including root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The results reveal an intriguing trend: both models exhibit superior performance when applied to the Ethereum dataset compared to the Bitcoin dataset. This observation suggests the potential presence of Ethereum-specific features or patterns that align more effectively with deep learning model architectures. Notably, the GRU model consistently outperforms the LSTM model across RMSE, MAE, and MAPE. These outcomes underscore the GRU model’s capacity as a robust tool for cryptocurrency value prediction. In summary, this study tackles the challenge of cryptocurrency price prediction while emphasizing the promising role of advanced neural network architectures, such as GRU, in enhancing prediction accuracy, thus offering valuable insights into financial forecasting.

This study aims to predict cryptocurrency prices using Long Short-Term Memory(LSTM) and Gated Recurrent Unit(GRU) for three different coins: BitCoin, Ethereum, and Litecoin. For the training data for prediction, two data sets with different statistical characteristics in terms of Kurtosis and Skewness are used. LSTM and GRU models are trained and tested on the same hyperparameter configuration while increasing the number of epochs from 1 to 30. The accuracy of each model is measured by Root Mean Square Error (RMSE) and MAE (Mean Absolute Error). As a result of comparing GRU and LSTM, in BTC and ETH, the GRU was more advantageous for the downward stabilization trend, and the LSTM was suitable for the upward stabilization trend. However, in case of low-priced LTC, LSTM and GRU showed the same performance in sample type A, and in the case of type B, GRU was more accurate.

Traffic flow prediction plays an important role in intelligent transportation systems. To accurately capture the complex non-linear temporal characteristics of traffic flow, this paper adopts a Bi-directional Gated Recurrent Unit (Bi-GRU) model in traffic flow prediction. Compared to Gated Recurrent Unit (GRU), which can memorize information from the previous sequence, this model can memorize the traffic flow information in both previous and subsequent sequence. To demonstrate the model’s performance, a set of real case data at 1-hour intervals from 5 working days was used, wherein the dataset was separated into training and validation. To improve data quality, an augmented dickey-fuller unit root test and differential processing were performed before model training. Four benchmark models were used, including the Autoregressive Integrated Moving Average (ARIMA), Long Short-Term Memory (LSTM), Bidirectional Long Short-Term Memory (Bi-LSTM), and GRU. The prediction results show the superior performance of Bi-GRU. The Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute Error (MAE) of the Bi-GRU model are 30.38, 9.88%, and 23.35, respectively. The prediction accuracy of LSTM, Bi-LSTM, GRU, and Bi-GRU, which belong to deep learning methods, is significantly higher than that of the traditional ARIMA model. The MAPE difference of Bi-GRU and GRU is 0.48% which is a small prediction error value. The results show that the prediction accuracy of the peak period is higher than that of the low peak. The Bi-GRU model has a certain lag on traffic flow prediction.

Highly accurate cryptocurrency price predictions are of paramount interest to investors and researchers. However, owing to the nonlinearity of the cryptocurrency market, it is difficult to assess the distinct nature of time-series data, resulting in challenges in generating appropriate price predictions. Numerous studies have been conducted on cryptocurrency price prediction using different Deep Learning (DL) based algorithms. This study proposes three types of Recurrent Neural Networks (RNNs): namely, Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Bi-Directional LSTM (Bi-LSTM) for exchange rate predictions of three major cryptocurrencies in the world, as measured by their market capitalization—Bitcoin (BTC), Ethereum (ETH), and Litecoin (LTC). The experimental results on the three major cryptocurrencies using both Root Mean Squared Error (RMSE) and the Mean Absolute Percentage Error (MAPE) show that the Bi-LSTM performed better in prediction than LSTM and GRU. Therefore, it can be considered the best algorithm. Bi-LSTM presented the most accurate prediction compared to GRU and LSTM, with MAPE values of 0.036, 0.041, and 0.124 for BTC, LTC, and ETH, respectively. The paper suggests that the prediction models presented in it are accurate in predicting cryptocurrency prices and can be beneficial for investors and traders. Additionally, future research should focus on exploring other factors that may influence cryptocurrency prices, such as social media and trading volumes.

Bangladesh, being a country that relies on agriculture, has its agricultural sector contributing around 20% to the Gross Domestic Product (GDP) and providing employment opportunities for nearly 60% of the population. The study proposes a novel multi-step forecasting deep-learning framework designed to forecast the maximum temperature and humidity of 24 cities, called Hierarchical Temporal Convolutional Long Short-Term Memory with attention (HTC-LSTM-Attn). The model contains hierarchical temporal convolutions (HTC) for extracting multi-scale patterns, bidirectional LSTMs for sequential dependencies, and an attention mechanism for learning to weigh time steps differently, while parameters are optimized with Keras tuner. Using data from Bangladesh Agricultural Research Council (BARC) from 1961 to 2022 and rigorous preprocessing with seasonal features and lagged statistics, the model obtains temperature results for with a Mean Absolute Error (MAE) of 0.8178 °C, Root Mean Squared Error (RMSE) of 0.9718 °C, R-squared (R²) of 0.8527, and Mean Absolute Percentage Error (MAPE) of 2.8823% and humidity with MAE of 2.4693%, RMSE of 3.2442%, R² of 0.7228, and MAPE of 3.1757% values on a strict temporal test set (19 stations, 2016–2022). On a spatial hold-out test set (5 unseen stations, 2016–2022) performance remains robust, temperature with MAE of 0.9587 °C, RMSE of 1.1898 °C, R² of 0.8342, and MAPE of 3.1534% and humidity with MAE of 2.4796%, RMSE of 3.2119%, R² of 0.6561, and MAPE of 3.2045% consistently surpassing performance measures of models Gated Recurrent Unit (GRU), Long Short-Term Memory (LSTM), Convolutional Neural Network (CNN), Decision Tree Regression (DTR), Convolutional Neural Network – Long Short-Term Memory (CNN-LSTM) and latest transformer-based architectures (Autoformer, FEDformer, TimesNet, and Pyraformer). These results have shown robust spatial performance with the respective improvements needed in agricultural planning and disaster management in Bangladesh, in its vulnerable climate context.