Forecasting, Volume 7, Issue 4 (December 2025) – 11 articles

In many different applications such as retail, energy, and tourism, forecasts for a set of related time series must satisfy both linear and non-negativity constraints, as negative values are meaningless in practice. Standard regression-based reconciliation approaches achieve coherence with linear constraints, but may generate negative forecasts, reducing interpretability and usability. This paper develops and evaluates three alternative strategies for non-negative forecast reconciliation. First, reconciliation is formulated as a non-negative least squares problem and solved with the operator splitting quadratic program, allowing flexible inclusion of additional constraints. Second, we propose an iterative non-negative reconciliation with immutable forecasts, offering a practical optimization-based alternative. Third, we investigate a family of set-negative-to-zero heuristics that achieve efficiency and interpretability at minimal computational cost. Using the Australian Tourism Demand dataset, we compare these approaches in terms of forecast accuracy and computation time. The results show that non-negativity constraints consistently improve accuracy compared to base forecasts. Overall, set-negative-to-zero achieve near-optimal performance with negligible computation time, the block principal pivoting algorithm provides a good accuracy–efficiency compromise, and the operator splitting quadratic program offers flexibility for incorporating additional constraints in large-scale applications. Full article

Accurate inflation forecasting is of central importance for monetary authorities, governments, and businesses, as it shapes economic decisions and policy responses. While most studies focus on headline inflation, this paper analyses the Harmonised Index of Consumer Prices (HICP) and its 12 subcomponents in the euro area over the period 2000–2023, covering episodes of financial crisis, economic stability, and recent inflationary shocks. We apply a broad set of machine learning and deep learning models, systematically optimized through grid search, and evaluate their performance using the Normalized Mean Absolute Error (NMAE). To complement traditional accuracy measures, we introduce the Forecastability Index (FI) and the Interquartile Range (IQR), which jointly capture both the difficulty and robustness of forecasts. Our results show that RNN and LSTM architectures consistently outperform traditional approaches such as SVR and RFR, particularly in volatile environments. Subcomponents such as Health and Education proved easier to forecast, while Recreation and culture and Restaurants and hotels were among the most challenging. The findings demonstrate that macroeconomic stability enhances forecasting accuracy, whereas crises amplify errors and inter-model dispersion. By highlighting the heterogeneous predictability of inflation subcomponents, this study provides novel insights with strong policy relevance, showing which categories can be forecast with greater confidence and where uncertainty requires more cautious intervention. Full article

Accurate forecasts of the U.S. renewable energy consumption mix are essential for planning transmission upgrades, sizing storage, and setting balancing market rules. We introduce a Bayesian Dirichlet ARMA model (BDARMA) tailored to monthly shares of hydro, geothermal, solar, wind, wood, municipal waste, and biofuels from January 2010 through January 2025. The mean vector is modeled with a parsimonious VAR(2) in additive log ratio space, while the Dirichlet concentration parameter follows an intercept plus five Fourier harmonics, allowing for seasonal widening and narrowing of predictive dispersion. Forecast performance is assessed with a 61-split rolling origin experiment that issues twelve month density forecasts from January 2019 to January 2024. Compared with three alternatives (a Gaussian VAR(2) fitted in transform space, a seasonal naive approach that repeats last year’s proportions, and a drift-free ALR random walk), BDARMA lowers the mean continuous ranked probability score by 15 to 60 percent, achieves componentwise 90 percent interval coverage near nominal, and maintains point accuracy (Aitchison RMSE) on par with the Gaussian VAR through eight months and within 0.02 units afterward. These results highlight BDARMA’s ability to deliver sharp and well-calibrated probabilistic forecasts for multivariate renewable energy shares without sacrificing point precision. Full article

Financial sustainability in higher education is increasingly fragile due to policy shifts, rising costs, and funding volatility. Legacy early-warning systems based on static thresholds or rules struggle to adapt to these dynamics and often overlook fairness and interpretability—two essentials in public-sector governance. We propose a university financial risk early-warning framework that couples a causal-attention Transformer with Multi-Objective Bayesian Optimization (MBO). The optimizer searches a constrained Pareto frontier to jointly improve predictive accuracy (AUC↑), fairness (demographic parity gap, DP_Gap↓), and computational efficiency (time↓). A sparse kernel surrogate (SKO) accelerates convergence in high-dimensional tuning; a dual-head output (risk probability and health score) and SHAP-based attribution enhance transparency and regulatory alignment. On multi-year, multi-institution data, the approach surpasses mainstream baselines in AUC, reduces DP_Gap, and yields expert-consistent explanations. Methodologically, the design aligns with LLM-style time-series forecasting by exploiting causal masking and long-range dependencies while providing governance-oriented explainability. The framework delivers earlier, data-driven signals of financial stress, supporting proactive resource allocation, funding restructuring, and long-term planning in higher education finance. Full article

Accurate precipitation forecasting plays a crucial role in sustainable water resource management, especially in arid regions like Konya, one of Turkey’s driest areas. Reliable forecasts support effective water budgeting, agricultural planning, and climate adaptation efforts in the region. This study investigates the performance of different deep learning training algorithms in forecasting monthly precipitation using Long Short-Term Memory (LSTM) networks, a method tailored for time-series prediction. A comprehensive dataset comprising 39 years (1984–2022) of precipitation records was utilized, obtained from the Turkish State Meteorological Service (MGM) as ground-based observations and from NASA’s POWER database as remote sensing data, and was split into 80% for training and 20% for testing. A comparative analysis of three widely used optimization algorithms, Adaptive Moment Estimation (ADAM), Root Mean Square Propagation (RMSProp), and Stochastic Gradient Descent with Momentum (SGDM), revealed that ADAM consistently outperformed the others in forecasting accuracy. Model performance was evaluated with statistical metrics, and the LSTM-ADAM combination achieved the best results. In the final phase, cross-validation was applied using MGM and NASA data sources in a crosswise manner to test model generalizability and data source independence. The best performance was observed when the model was trained with MGM data and tested with NASA data, achieving a remarkably low RMSE of 3.62 mm, MAE of 2.93 mm, R² of 0.9966, and NSE of 0.9686. When trained with NASA data and tested with MGM data, the model still demonstrated strong performance, with an RMSE of 4.48 mm, MAE of 3.22 mm, R² of 0.9921, and NSE of 0.9678. These results demonstrate that satellite and ground-based data can be used interchangeably under suitable conditions, while also confirming the superiority of the ADAM optimizer in LSTM-based precipitation forecasting. Full article

This study evaluates the effect of simple data-level balancing techniques on predicting school dropout across all state public high schools in Espírito Santo, Brazil. We trained Logistic Regression with LASSO (LR), Random Forest (RF), and Naive Bayes (NB) models on first-quarter data from 2018–2019 and forecasted dropouts for 2020, with additional validation in 2022. Facing strong class imbalance, we compared three balancing methods—RUS, SMOTE, and ROSE—against models trained on the original data. Performance was assessed using accuracy, sensitivity, specificity, precision, F1, AUC, and G-mean. Results show that the imbalance severely harmed RF and NB trained without balancing, while Logistic Regression remained more stable. Overall, balancing techniques improved most metrics: RUS and ROSE were often superior, while SMOTE produced mixed results. Optimal configurations varied by year and metric, and RUS and ROSE made up most of the best combinations. Although most configurations benefited from balancing, some decreased performance; therefore, we recommend systematic testing of multiple balancing strategies and further research into SMOTE variants and algorithm-level approaches. Full article

As the world is shifting toward cleaner energy sources, accurate forecasting of solar radiation is critical for optimizing the performance and integration of solar energy systems. In this study, we explore eight machine learning models, namely, Random Forest Regressor, Linear Regression Model, Artificial Neural Network, k-Nearest Neighbors, Support Vector Regression, Gradient Boosting Regressor, Gaussian Process Regression, and Deep Learning, as to their use in forecasting direct solar radiation across six climatically diverse regions in the Kingdom of Saudi Arabia. The models were evaluated using eight statistical metrics along with time-series and absolute error analyses. A key contribution of this work is the introduction of Trigonometric Cyclical Encoding, which has significantly improved temporal representation learning. Comparative SHAP-based feature-importance analysis revealed that Trigonometric Cyclical Encoding enhanced the explanatory power of temporal features by 49.26% for monthly cycles and 53.30% for daily cycles. The findings show that Deep Learning achieved the lowest root mean square error, as well as the highest coefficient of determination, while Artificial Neural Network demonstrated consistently high accuracy across the sites. Support Vector Regression performed optimally but was less reliable in some regions. Error and time-series analyses reveal that Artificial Neural Network and Deep Learning maintained stable prediction accuracy throughout high solar radiation seasons, whereas Linear Regression, Random Forest Regressor, and k-Nearest Neighbors showed greater fluctuations. The proposed Trigonometric Cyclical Encoding technique further enhanced model performance by maintaining the overall fitness of the models, which ranged between 81.79% and 94.36% in all scenarios. This paper supports the effective planning of solar energy and integration in challenging climatic conditions. Full article

Positive percentage time series are present in many empirical applications; they take values in the continuous interval (0,1) and are often modeled with linear dynamic models. Risks of biased predictions (outside the admissible range) and problems of heteroskedasticity in the presence of asymmetric distributions are ignored by practitioners. Alternative models are proposed in the statistical literature; the most suitable is the dynamic beta regression which belongs to generalized linear models (GLM) and uses the logit transformation as a link function. However, owing to the Jensen inequality, this approach may also not be optimal in prediction; thus, the aim of the present paper is the in-depth forecasting comparison of linear and beta autoregressions. Simulation experiments and applications to nonstationary time series (the US unemployment rate and BR hydroelectric energy) are carried out. Rolling regression for time-varying parameters is applied to both linear and beta models, and a prediction criterion for the joint selection of model order and sample size is defined. Full article

This research introduces a system designed to predict three-dimensional airspace occupancy over Colombia using historical Automatic Dependent Surveillance-Broadcast (ADS-B) data and machine learning techniques. The goal is to support proactive air traffic management by estimating future aircraft positions—specifically their latitude, longitude, and flight level. To achieve this, four predictive models were developed and tested: K-Nearest Neighbors (KNN), Random Forest, Extreme Gradient Boosting (XGBoost), and Long Short-Term Memory (LSTM). Among them, the LSTM model delivered the most accurate results, with a Mean Absolute Error (MAE) of 312.59, a Root Mean Squared Error (RMSE) of 1187.43, and a coefficient of determination (R²) of 0.7523. Compared to the baseline models (KNN, Random Forest, XGBoost), these values represent an improvement of approximately 91% in MAE, 83% in RMSE, and an eighteen-fold increase in R², demonstrating the substantial advantage of the LSTM approach. These metrics indicate a significant improvement over the other models, particularly in capturing temporal patterns and adjusting to evolving traffic conditions. The strength of the LSTM approach lies in its ability to model sequential data and adapt to dynamic environments—making it especially suitable for supporting future Trajectory-Based Operations (TBO). The results confirm that predicting airspace occupancy in three dimensions using historical data are not only possible but can yield reliable and actionable insights. Looking ahead, the integration of hybrid neural network architectures and their deployment in real-time systems offer promising directions to enhance both accuracy and operational value. Full article

Financial time-series prediction remains a significant challenge, driven by market volatility, nonlinear dynamic characteristics, and the complex interplay between quantitative indicators and investor sentiment. Traditional time-series models (e.g., ARIMA and GARCH) struggle to capture the nuanced sentiment in textual data, while static deep learning integration methods fail to adapt to market regime transitions (bull markets, bear markets, and consolidation). This study proposes a hybrid framework that integrates investor forum sentiment analysis with adaptive deep reinforcement learning (DRL) for dynamic model integration. By constructing a domain-specific financial sentiment dictionary (containing 16,673 entries) based on the sentiment analysis approach and word-embedding technique, we achieved up to 97.35% accuracy in forum title classification tasks. Historical price data and investor forum sentiment information were then fed into a Support Vector Regressor (SVR) and three Transformer variants (single-layer, multi-layer, and bidirectional variants) for predictions, with a Deep Q-Network (DQN) agent dynamically fusing the prediction results. Comprehensive experiments were conducted on diverse financial datasets, including China Unicom, the CSI 100 index, corn, and Amazon (AMZN). The experimental results demonstrate that our proposed approach, combining textual sentiment with adaptive DRL integration, significantly enhances prediction robustness in volatile markets, achieving the lowest RMSEs across diverse assets. It overcomes the limitations of static methods and multi-market generalization, outperforming both benchmark and state-of-the-art models. Full article

Wholesale sales value is one of the key elements included in the coincident indicator series of the indexes of business conditions in Japan. The objectives of this study are twofold. The first is to comprehend features of dynamic structure of various components for 12 business types of the wholesale sales in Japan, focusing on the period from January 1980 to December 2022. The second is to elucidate effect of business cycles on the behavior of each business type of wholesale sales. Specifically, we utilize our moving linear model approach to decompose monthly time-series data of wholesale sales into a seasonal component, an unusually varying component containing outliers, a constrained component, and a remaining component. Additionally, we construct a distribution-free dynamic linear model and examine the time-varying relationship between the decomposed remaining component, which contains cyclical variation, in each business type of the wholesale sales and that in the coincident composite index. Our proposed approach reveals complex dynamics of various components of time series on wholesale sales. Furthermore, we find that different business types of the wholesale sales exhibit diverse responses to business cycles, which are influenced by macroeconomic conditions, government policies, or exogenous shocks. Full article