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A special issue of Forecasting (ISSN 2571-9394).

Deadline for manuscript submissions: closed (31 December 2025) | Viewed by 26131

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Special Issue Editor

Prof. Dr. Sonia Leva

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Guest Editor

Department of Energy, Politecnico di Milano, 20156 Milan, Italy
Interests: photovoltaic system; grid; power sharing; inverters; forecasting; nowcasting; machine learning; degradation; battery management systems; polymer solar cells; organic photovoltaics; electric vehicle; vehicle-to-grid; microgrid; energy systems; maximum power point trackers; electric power plant loads; electricity price; power markets; heterogeneous networks; base stations; energy efficiency; life cycle assessment; wind power; regenerative braking; bicycles; motorcycles; car sharing; autonomous vehicles
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Special Issue Information

Dear Colleagues,

As the Editor-in-Chief of Forecasting, I am glad to announce the Special Issue "Feature Papers of Forecasting 2025". This Special Issue is designed to publish high-quality papers in forecasting. We welcome submissions from Editorial Board Members and outstanding scholars invited by the Editorial Board and the Editorial Office. The scope of this Special Issue includes, but is not limited to, the following topics: power and energy forecasting; forecasting in economics and management; forecasting in computer science; weather and forecasting; and environmental forecasting.

We will select 10–20 papers in 2025 from excellent scholars around the world to publish for free for the benefit of both authors and readers.

You are welcome to send short proposals for submissions of feature papers to our Editorial Office (forecasting@mdpi.com). They will first be evaluated by academic editors, and, then, selected papers will be thoroughly and rigorously peer reviewed.

Prof. Dr. Sonia Leva
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Forecasting is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

power and energy forecasting
forecasting in economics and management
forecasting in computer science
weather and forecasting
environmental forecasting

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Published Papers (10 papers)

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Research

28 pages, 4067 KB

Open AccessArticle

Machine Learning Forecasting of Strong Subsequent Events in New Zealand Using the NESTORE Algorithm

by Letizia Caravella and Stefania Gentili

Forecasting 2026, 8(1), 16; https://doi.org/10.3390/forecast8010016 - 12 Feb 2026

Viewed by 1283

Abstract

New Zealand, located along the boundary between the Pacific and Australian plates, is among the most seismically active regions in the world. In such an area, reliable short-term forecasting of strong aftershocks is essential for seismic risk mitigation. In this study, we apply NESTORE (NExt STrOng Related Earthquake), a machine learning probabilistic forecasting algorithm, to the New Zealand earthquake catalogue to evaluate the probability that a mainshock of magnitude M_m will be followed by an event of magnitude ≥ M_m − 1 within a defined space–time window. NESTORE uses nine features describing early post-mainshock seismicity and outputs the probability that a cluster is Type A (i.e., containing a strong aftershock) or not (Type B). We assess performance using two testing strategies: chronological training–testing splits and k-fold cross-validation and refine the training set using the REPENESE outlier-detection procedure. The k-fold approach proves more robust than the chronological one, despite changes in catalogue characteristics over time. Eighteen hours after the mainshock, NESTORE correctly classified 88% of clusters (75% for Type A and 92% for Type B; Precision = 0.75). Notably, the highly destructive 2010–2011 Canterbury–Christchurch sequence was correctly identified as Type A. These findings support the applicability of NESTORE for short-term aftershock forecasting in New Zealand. Full article

(This article belongs to the Special Issue Feature Papers of Forecasting 2025)

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20 pages, 3520 KB

Open AccessArticle

Multi-Scale Explainable AI for RMB Exchange Rate Drivers

by Jie Ji, Shouyang Wang and Yunjie Wei

Forecasting 2026, 8(1), 7; https://doi.org/10.3390/forecast8010007 - 21 Jan 2026

Viewed by 882

Abstract

To address the nonlinear nature of exchange rates where drivers vary by time horizon, this paper proposes a CEEMDAN-PE-CatBoost-SHAP framework. Analyzing USD/CNY data (2012–2024), we decomposed rates into high, medium, and low frequencies to bridge machine learning with economic interpretability. Empirical results revealed distinct frequency-dependent drivers: high-frequency fluctuations depend on market sentiment; medium-frequency variations follow Fed policies; and low-frequency trends reflect fundamentals like gold prices. SHAP analysis provides transparent attribution of these factors. This multi-scale approach isolates heterogeneous drivers, offering policymakers and investors a nuanced paradigm for managing currency risks. The study significantly clarifies how different economic factors shape exchange rate dynamics across varying time scales. Full article

(This article belongs to the Special Issue Feature Papers of Forecasting 2025)

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29 pages, 3003 KB

Open AccessArticle

Pollutant-Specific Deep Learning Architectures for Multi-Species Air Quality Bias Correction: Application to NO₂ and PM₁₀ in California

by Ioannis Stergiou, Nektaria Traka, Dimitrios Melas, Efthimios Tagaris and Rafaella-Eleni P. Sotiropoulou

Forecasting 2026, 8(1), 5; https://doi.org/10.3390/forecast8010005 - 9 Jan 2026

Viewed by 1354

Abstract

Accurate air quality forecasting remains challenging due to persistent biases in chemical transport models. Addressing this challenge, the current study develops pollutant-specific deep learning frameworks that correct systematic errors in the Community Multiscale Air Quality (CMAQ) simulations of nitrogen dioxide (NO₂) and coarse particulate matter (PM₁₀) over California. Building upon a previous study on ozone bias correction, a hybrid CNN–Attention–LSTM architecture is adapted, and a weighted Huber loss function is introduced for PM₁₀ to enhance the detection of extreme pollution events through a gated tail-weighting mechanism. Using data from twenty EPA monitoring stations (ten per pollutant) for 2010–2014, the proposed approach achieves substantial performance gains over the CMAQ baseline. For NO₂, RMSE decreases by ~51% with an average systematic bias reduction of ~80% and a random error reduction of ~42%. For PM₁₀, RMSE improves by ~49% while the systematic and random errors decrease by ~94% and ~33%, respectively. The PM₁₀ model also shows high consistency with observations (Index of Agreement improvement of ~105%) and a strong ability to capture peak events (F1 score improvement of ~270%), while the NO₂ model achieves large gains in explanatory power (R² improvement averaging ~816%). Both pollutants also demonstrate enhanced temporal agreement between predictions and observations, as confirmed by the Dynamic Time Warping analysis (NO₂: ~55%, PM₁₀: ~58%). These results indicate that pollutant-specific loss functions and architectural tuning can significantly improve both accuracy and event sensitivity, offering a transferable framework for bias correction across multiple pollutants and regions. Full article

(This article belongs to the Special Issue Feature Papers of Forecasting 2025)

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21 pages, 7395 KB

Open AccessArticle

A New Loss Function for Enhancing Peak Prediction in Time Series Data with High Variability

by Mahan Hajiabbasi Somehsaraie, Soheyla Tofighi, Zhaoan Wang, Jun Wang and Shaoping Xiao

Forecasting 2025, 7(4), 75; https://doi.org/10.3390/forecast7040075 - 3 Dec 2025

Cited by 2 | Viewed by 3137

Abstract

Time series models are considered among the most intricate models in machine learning. Due to sharp temporal variations, time series models normally fall short in predicting the peaks or local minima accurately. To overcome this challenge, we proposed a novel custom loss function, Enhanced Peak (EP) loss, specifically designed to pinpoint peaks and troughs in time series models, to address underestimations and overestimations in the forecasting process. EP loss applies an adaptive penalty when prediction errors exceed a specified threshold, encouraging the model to focus more effectively on these regions. To evaluate the effectiveness and versatility of EP loss, the loss function was tested on three highly variable datasets: NO_x emissions, streamflow measurements, and gold price, implementing Gated Recurrent Unit and Transformer-based models. The results consistently demonstrated that EP loss significantly mitigates peak prediction errors compared to conventional loss functions, highlighting its potential for highly variable time series applications. Full article

(This article belongs to the Special Issue Feature Papers of Forecasting 2025)

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29 pages, 835 KB

Open AccessArticle

Non-Negative Forecast Reconciliation: Optimal Methods and Operational Solutions

by Daniele Girolimetto

Forecasting 2025, 7(4), 64; https://doi.org/10.3390/forecast7040064 - 26 Oct 2025

Cited by 1 | Viewed by 2023

Abstract

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

(This article belongs to the Special Issue Feature Papers of Forecasting 2025)

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17 pages, 887 KB

Open AccessArticle

Comparison of Linear and Beta Autoregressive Models in Forecasting Nonstationary Percentage Time Series

by Carlo Grillenzoni

Forecasting 2025, 7(4), 57; https://doi.org/10.3390/forecast7040057 - 13 Oct 2025

Cited by 1 | Viewed by 1466

Abstract

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 article belongs to the Special Issue Feature Papers of Forecasting 2025)

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36 pages, 4934 KB

Open AccessArticle

SGR-Net: A Synergistic Attention Network for Robust Stock Market Forecasting

by Rasmi Ranjan Khansama, Rojalina Priyadarshini, Surendra Kumar Nanda, Rabindra Kumar Barik and Manob Jyoti Saikia

Forecasting 2025, 7(3), 50; https://doi.org/10.3390/forecast7030050 - 14 Sep 2025

Cited by 1 | Viewed by 2011

Abstract

Owing to the high volatility, non-stationarity, and complexity of financial time-series data, stock market trend prediction remains a crucial but difficult endeavor. To address this, we present a novel Multi-Perspective Fused Attention model (SGR-Net) that amalgamates Random, Global, and Sparse Attention mechanisms to improve stock trend forecasting accuracy and generalization capability. The proposed Fused Attention model (SGR-Net) is trained on a rich feature space consisting of thirteen widely used technical indicators derived from raw stock index prices to effectively classify stock index trends as either uptrends or downtrends. Across nine global stock indices—DJUS, NYSE AMEX, BSE, DAX, NASDAQ, Nikkei, S&P 500, Shanghai Stock Exchange, and NIFTY 50—we evaluated the proposed model and compared it against baseline deep learning techniques, which include LSTM, GRU, Vanilla Attention, and Self-Attention. Experimental results across nine global stock index datasets show that the Fused Attention model produces the highest accuracy of 94.36% and AUC of 0.9888. Furthermore, even at lower epochs of training, i.e., 20 epochs, the proposed Fused Attention model produces faster convergence and better generalization, yielding an AUC of 0.9265, compared with 0.9179 for Self-Attention, on the DJUS index. The proposed model also demonstrates competitive training time and noteworthy performance on all nine stock indices. This is due to the incorporation of Sparse Attention, which lowers computation time to 57.62 s, only slightly more than the 54.22 s required for the Self-Attention model on the Nikkei 225 index. Additionally, the model incorporates Global Attention, which captures long-term dependencies in time-series data, and Random Attention, which addresses the problem of overfitting. Overall, this study presents a robust and reliable model that can help individuals, research communities, and investors identify profitable stocks across diverse global markets. Full article

(This article belongs to the Special Issue Feature Papers of Forecasting 2025)

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19 pages, 4920 KB

Open AccessArticle

NCD-Pred: Forecasting Multichannel Shipboard Electrical Power Demand Using Neighborhood-Constrained VMD

by Paolo Fazzini, Giuseppe La Tona, Marco Montuori, Matteo Diez and Maria Carmela Di Piazza

Forecasting 2025, 7(3), 44; https://doi.org/10.3390/forecast7030044 - 13 Aug 2025

Cited by 1 | Viewed by 1382

Abstract

This paper introduces Neighborhood-Constrained Decomposition-based Prediction (NCD-Pred), the first system to leverage Neighborhood-Constrained Variational Mode Decomposition (NCVMD) for multichannel forecasting by integrating time series decomposition and neural networks. NCD-Pred leverages NCVMD to decompose a multichannel signal into simpler, band-limited components—referred to as intrinsic mode functions or simply modes—by prioritizing the most informative channel (the main channel) over less informative ones (the auxiliary channels) and bringing their central frequencies into alignment up to a tunable extent. This frequency synchronization provides a framework for cooperative mode forecasting, where predictions of signal components are recombined to produce the original signal prediction. For mode-level forecasting, Long Short-Term Memory (LSTM) networks are utilized. NCD-Pred’s performance is evaluated against similarly designed mode-level forecasting systems using a multichannel dataset with weak cross-correlation, representing power load on a large vessel. The results show that NCD-Pred outperforms benchmark methods, demonstrating its practical utility in real signal processing scenarios. Full article

(This article belongs to the Special Issue Feature Papers of Forecasting 2025)

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31 pages, 1127 KB

Open AccessArticle

Optimizing Credit Risk Prediction for Peer-to-Peer Lending Using Machine Learning

by Lyne Imene Souadda, Ahmed Rami Halitim, Billel Benilles, José Manuel Oliveira and Patrícia Ramos

Forecasting 2025, 7(3), 35; https://doi.org/10.3390/forecast7030035 - 29 Jun 2025

Cited by 4 | Viewed by 7171

Abstract

Hyperparameter optimization (HPO) is critical for enhancing the predictive performance of machine learning models in credit risk assessment for peer-to-peer (P2P) lending. This study evaluates four HPO methods, Grid Search, Random Search, Hyperopt, and Optuna, across four models, Logistic Regression, Random Forest, XGBoost, and LightGBM, using three real-world datasets (Lending Club, Australia, Taiwan). We assess predictive accuracy (AUC, Sensitivity, Specificity, G-Mean), computational efficiency, robustness, and interpretability. LightGBM achieves the highest AUC (e.g.,

70.77 %

on Lending Club,

93.25 %

on Australia,

77.85 %

on Taiwan), with XGBoost performing comparably. Bayesian methods (Hyperopt, Optuna) match or approach Grid Search’s accuracy while reducing runtime by up to

75.7

-fold (e.g.,

3.19

vs.

241.47

min for LightGBM on Lending Club). A sensitivity analysis confirms robust hyperparameter configurations, with AUC variations typically below

0.4 %

under

\pm 10 %

perturbations. A feature importance analysis, using gain and SHAP metrics, identifies debt-to-income ratio and employment title as key default predictors, with stable rankings (Spearman correlation

> 0.95, p < 0.01

) across tuning methods, enhancing model interpretability. Operational impact depends on data quality, scalable infrastructure, fairness audits for features like employment title, and stakeholder collaboration to ensure compliance with regulations like the EU AI Act and U.S. Equal Credit Opportunity Act. These findings advocate Bayesian HPO and ensemble models in P2P lending, offering scalable, transparent, and fair solutions for default prediction, with future research suggested to explore advanced resampling, cost-sensitive metrics, and feature interactions. Full article

(This article belongs to the Special Issue Feature Papers of Forecasting 2025)

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27 pages, 3332 KB

Open AccessArticle

Wind Speed Forecasting with Differentially Evolved Minimum-Bandwidth Filters and Gated Recurrent Units

by Khathutshelo Steven Sivhugwana and Edmore Ranganai

Forecasting 2025, 7(2), 27; https://doi.org/10.3390/forecast7020027 - 10 Jun 2025

Cited by 2 | Viewed by 2702

Abstract

Wind data are often cyclostationary due to cyclic variations, non-constant variance resulting from fluctuating weather conditions, and structural breaks due to transient behaviour (due to wind gusts and turbulence), resulting in unreliable wind power supply. In wavelet hybrid forecasting, wind prediction accuracy depends [...] Read more.

L

) and the wavelet filter technique selected. Hence, we examined the efficacy of wind predictions as a function of

L

and wavelet filters. In the proposed hybrid approach, differential evolution (DE) optimises the decomposition level of various wavelet filters (i.e., least asymmetric (LA), Daubechies (DB), and Morris minimum-bandwidth (MB)) using the maximal overlap discrete wavelet transform (MODWT), allowing for the decomposition of wind data into more statistically sound sub-signals. These sub-signals are used as inputs into the gated recurrent unit (GRU) to accurately capture wind speed. The final predicted values are obtained by reconciling the sub-signal predictions using multiresolution analysis (MRA) to form wavelet-MODWT-GRUs. Using wind data from three Wind Atlas South Africa (WASA) locations, Alexander Bay, Humansdorp, and Jozini, the root mean square error, mean absolute error, coefficient of determination, probability integral transform, pinball loss, and Dawid-Sebastiani showed that the MB-MODWT-GRU at

L = 3

was best across the three locations. Full article

(This article belongs to the Special Issue Feature Papers of Forecasting 2025)

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