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Search Results (204)

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20 pages, 2048 KB  
Article
Laminarity and Market Stress: Testing an RQA-Based Diagnostic During the COVID-19 Shock
by Domenico Vicinanza
J. Risk Financial Manag. 2026, 19(6), 430; https://doi.org/10.3390/jrfm19060430 - 15 Jun 2026
Viewed by 131
Abstract
Financial crises are usually identified through drawdowns, volatility, and changes in returns, but these indicators do not directly describe whether the recurrence structure of market behaviour changes during a shock. This study tests Laminarity, a Recurrence Quantification Analysis measure derived from vertical structures [...] Read more.
Financial crises are usually identified through drawdowns, volatility, and changes in returns, but these indicators do not directly describe whether the recurrence structure of market behaviour changes during a shock. This study tests Laminarity, a Recurrence Quantification Analysis measure derived from vertical structures in recurrence plots, as a nonlinear diagnostic of persistence and market-regime structure during the COVID-19 market shock. Daily data for the Dow Jones Industrial Average, S&P 500, and NASDAQ Composite from 2018 to 2022 are analysed using adjusted prices and log returns. Rolling-window Recurrence Quantification Analysis is applied across alternative window lengths and recurrence thresholds, testing crisis-responsive and longer robustness windows, as well as sparse, intermediate, and denser recurrence definitions. Drawdown and rolling volatility are used as descriptive benchmarks for cumulative loss and fluctuation intensity over the same stress episode. The results show that conventional indicators identify the COVID-19 shock clearly. Price-based Laminarity generally increases during the stress period, consistent with a more persistent crisis trajectory in price levels. Return-based Laminarity is more heterogeneous, with some specifications showing Laminarity loss and others increases. The findings do not support Laminarity as a universal crisis-warning signal, but as a parameter-sensitive diagnostic of recurrence structure, especially when interpreted alongside related RQA metrics. Full article
(This article belongs to the Special Issue Innovative Approaches to Financial Modeling and Decision-Making)
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39 pages, 5848 KB  
Article
Realized Volatility Forecasting in the Spanish Electricity Market During the 2021–2025 Energy Crisis
by David Veloso-Castello and J. Carlos García-Díaz
Mathematics 2026, 14(12), 2100; https://doi.org/10.3390/math14122100 - 11 Jun 2026
Viewed by 214
Abstract
This paper analyzes volatility forecasting in the Spanish electricity spot market over the period 2021–2025, characterized by uncertainty, frequent price jumps, and the increasing occurrence of zero and negative prices. To accommodate these features, electricity prices are shifted to ensure well-defined log-returns, and [...] Read more.
This paper analyzes volatility forecasting in the Spanish electricity spot market over the period 2021–2025, characterized by uncertainty, frequent price jumps, and the increasing occurrence of zero and negative prices. To accommodate these features, electricity prices are shifted to ensure well-defined log-returns, and predictable intraday and seasonal patterns are removed using the Ullrich demeaning procedure. Daily realized volatility measures are constructed from high-frequency data, including jump-robust and noise-robust estimators such as Median Realized Volatility and Realized Kernel. A broad set of volatility models, comprising GARCH-type specifications and multiple extensions of the Heterogeneous Autoregressive (HAR) framework, is evaluated using a coherent out-of-sample forecasting procedure. Model comparison is conducted through the Model Confidence Set methodology based on the QLIKE loss function, which identifies a Superior Set of Models with equal predictive ability. Conditional diagnostics, including Out-of-Sample ROOS2 measures and Mincer–Zarnowitz regressions, are subsequently used to characterize forecast accuracy, unbiasedness, and efficiency. The empirical results show that all GARCH models are systematically excluded from the superior set, while HAR-type specifications based on realized volatility dominate. Within this set, a HAR model incorporating Median Realized Volatility, jump components, and day-of-the-week effects delivers the strongest economic performance, achieving an Out-of-Sample ROOS 2 close to 0.5 with unbiased forecasts. Overall, the findings highlight the importance of long-memory dynamics, discontinuous price movements, and residual weekly seasonality for volatility forecasting in modern electricity markets. Full article
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17 pages, 867 KB  
Article
Energy and Logistics Cost Transmission in the Dairy Market: Evidence from Kazakhstan Using a Log-Linear ARDL Model
by Dauren Turarov, Zhumakul Abisheva, Aiman Issayeva, Madina Beisenova and Stefan Dyrka
Logistics 2026, 10(6), 121; https://doi.org/10.3390/logistics10060121 - 2 Jun 2026
Viewed by 534
Abstract
Background: This study aims to evaluate the impact of energy and logistics factors on the milk producer price index to support evidence-based policies that maintain price stability at an optimal level. Methods: Annual data for 2000–2023 are used, including the milk producer price [...] Read more.
Background: This study aims to evaluate the impact of energy and logistics factors on the milk producer price index to support evidence-based policies that maintain price stability at an optimal level. Methods: Annual data for 2000–2023 are used, including the milk producer price index, milk production volume, transport CPI, diesel price, CO2 emissions from agriculture, and renewable energy consumption (percentage of total energy consumption). A log-linear ARDL model is applied to examine both short- and long-run asymmetric effects of diesel prices, transport costs, and agricultural CO2 emissions on milk production dynamics. Results: The research results indicate that energy expenses, logistics considerations, and environmental metrics have statistically significant asymmetric influences on milk production. This underscores the varying short-term adjustments and enduring long-term economic effects throughout the supply chain. Conclusions: Energy and cost factors on the supply side significantly influence the stability of milk markets. Therefore, improving transportation efficiency, encouraging the use of renewable energy sources, and addressing environmental impacts can contribute to consistent and sustainable pricing. Specific policies—including investments in transport infrastructure, subsidies for green energy targeting dairy producers, carbon pricing with support tailored to the sector, and digitalization of supply chains—can enhance resilience and ensure price stability. Full article
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14 pages, 531 KB  
Article
The Impact of Economic Distress on Primary Headache Visits Under the Strain of the COVID-19 Pandemic: A Retrospective Study
by Merih Can Yilmaz, Ozgur Ozaydin and Keramettin Aydin
J. Clin. Med. 2026, 15(11), 4181; https://doi.org/10.3390/jcm15114181 - 28 May 2026
Viewed by 194
Abstract
Background and Objectives: Macroeconomic instability, particularly income loss, inflation and unemployment, is increasingly recognized as a psychosocial stressor that may influence both symptom burden and healthcare-seeking behavior. This single-center study investigated the association of income, inflation and unemployment with private-sector hospital visits [...] Read more.
Background and Objectives: Macroeconomic instability, particularly income loss, inflation and unemployment, is increasingly recognized as a psychosocial stressor that may influence both symptom burden and healthcare-seeking behavior. This single-center study investigated the association of income, inflation and unemployment with private-sector hospital visits for primary headache disorders and assessed whether economic stressors were associated with different patterns across demographic groups. Materials and Methods: We conducted a single-center, retrospective, ecological quarterly time-series analysis of hospital visits for primary headache disorders between 2016 and 2024 in a private tertiary care hospital in Turkey. After exclusions, 18,522 eligible hospital-visit records were included and categorized by sex and age (<18, 18–64, and ≥65 years). National data on real gross domestic product (GDP), consumer price index (CPI), unemployment and a COVID-19 period indicator were used. Counts were modeled with log-linked Poisson or negative binomial generalized linear models selected through overdispersion diagnostics, with seasonal controls and HAC-robust inference. Results: In most groups, higher GDP was associated with more primary headache visits, whereas higher inflation was consistently associated with fewer visits. The association with unemployment was heterogeneous: visits decreased significantly among the working-age population but increased among older adults. Contemporaneous models outperformed one-quarter lagged alternatives, suggesting that private-sector healthcare seeking may change within the same quarter as macroeconomic shocks. Conclusions: In this private hospital setting, macroeconomic deterioration was associated with reduced primary headache visits, particularly among working-age patients. These findings suggest that financial constraints may suppress private-sector healthcare utilization despite possible increases in stress-related symptoms, and that private hospital data may underestimate headache-related healthcare need during economic crises. Full article
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22 pages, 1538 KB  
Article
Construction Input Price Forecasting for Probabilistic Contingency Estimation in a Road Infrastructure Bridge Case Study
by Victor Andre Ariza Flores, Diego Pinedo, Alan Orellana and Amador Pinedo
Buildings 2026, 16(11), 2124; https://doi.org/10.3390/buildings16112124 - 26 May 2026
Viewed by 310
Abstract
Road infrastructure projects are frequently affected by cost overruns driven by volatility in critical construction inputs and by the uneven association between external market shocks and material price movements. However, existing studies still provide limited evidence on how comparative forecasting, temporal price-signal diagnostics [...] Read more.
Road infrastructure projects are frequently affected by cost overruns driven by volatility in critical construction inputs and by the uneven association between external market shocks and material price movements. However, existing studies still provide limited evidence on how comparative forecasting, temporal price-signal diagnostics and probabilistic simulation can be integrated into a contingency-oriented decision framework. This study examines how construction input price forecasting and probabilistic simulation can inform contingency estimation in a road infrastructure case study. The empirical application is based on a Peruvian bridge project and combines benchmark-oriented forecasting using Bi-GRU and Random Walk models, descriptive temporal diagnostics based on lead–lag assessment and rolling-correlation analysis, and Monte Carlo simulation. Monthly series for structural steel, construction steel, cement, and diesel were transformed into log-returns and evaluated under a strict chronological design, while oil, the exchange rate, and the consumer price index were incorporated as exogenous variables. The Random Walk model produced lower forecasting errors for most inputs, achieving lower RMSE values in seven of the eight input-period comparisons; Bi-GRU outperformed it only for diesel in the test subset, with a 7.24% lower RMSE. From a project cost-risk perspective, the P95 contingency was estimated at 3.92% under Bi-GRU and 3.96% under Random Walk, indicating a similar upper-percentile contingency envelope under both forecasting specifications. The findings support contingency as a confidence-based budgeting decision rather than a fixed percentage. Full article
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23 pages, 1054 KB  
Article
Red Grape Pomace as a Quality-Modulating Ingredient in Dairy Cattle Salamis
by Gabriele Busetta, Giuseppe Maniaci, Marcella Barbera, Cristina Giosuè, Simone Italia, Daniela Piazzese, Luca Settanni, Marco Alabiso and Raimondo Gaglio
Foods 2026, 15(10), 1792; https://doi.org/10.3390/foods15101792 - 19 May 2026
Viewed by 1541
Abstract
This study investigated the effects of red grape pomace powder (GPP) on spontaneously fermented salamis produced from the meat of retired cows and young bulls of the Cinisara dairy breed. The use of GPP and meat from these animal categories was motivated by [...] Read more.
This study investigated the effects of red grape pomace powder (GPP) on spontaneously fermented salamis produced from the meat of retired cows and young bulls of the Cinisara dairy breed. The use of GPP and meat from these animal categories was motivated by the valorization of low-commercial-value agri-food resources and the enhancement of sustainable local production chains. Plate count analyses showed typical fermentation dynamics, with lactic acid bacteria (LAB), coagulase-negative staphylococci, and yeasts reaching approximately 7 log CFU/g, and confirmed the absence of major foodborne pathogens. Illumina sequencing further characterized the bacterial community, identifying Latilactobacillus as the dominant genus at the end of ripening, with relative abundance (RA) of up to 65% in GPP-enriched trials. Physicochemical analyses showed progressive changes during ripening, including weight loss, pH decrease, color development, and increased proteolysis. GPP supplementation contributed to the stabilization of a*, chroma, and hue values, while reducing lightness during ripening. Oxidative stability measurements showed that GPP derived polyphenols effectively limited oxidative reactions, especially secondary lipid oxidation. GPP also modulated the volatile profile by increasing ester formation and introducing plant-derived compounds. Sensory evaluation revealed higher color intensity and aroma in enriched salamis, along with higher bitterness and lower structural homogeneity, especially in those produced from retired cows. Consumer surveys conducted in two retail settings indicated strong interest in this innovation, with over 80% of respondents willing to pay a 10–20% price premium. Overall, GPP emerges as a promising functional ingredient for enhancing, diversifying, and valorizing fermented salamis produced from dairy cattle meat, supporting both product innovation and sustainability-oriented strategies. Full article
(This article belongs to the Section Meat)
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17 pages, 479 KB  
Article
An Analytical Approximation of Warrant Prices via GARCH Models
by Noppanon Teangthae and Dawud Thongtha
AppliedMath 2026, 6(5), 72; https://doi.org/10.3390/appliedmath6050072 - 7 May 2026
Viewed by 399
Abstract
A warrant is a financial derivative that grants the holder the right to purchase company shares at a predetermined price within a specified period. Generally, upon exercise, the total number of outstanding shares increases because of the issuance of new shares, reducing the [...] Read more.
A warrant is a financial derivative that grants the holder the right to purchase company shares at a predetermined price within a specified period. Generally, upon exercise, the total number of outstanding shares increases because of the issuance of new shares, reducing the stock price. In this study, an analytical formula for warrant valuation is developed without relying on the restrictive assumptions of log-normal asset return distributions or constant volatility. The model incorporates key financial variables, including the current asset price, the strike price, the risk-free interest rate, the time to maturity, and the dilution factor. To capture dynamic market conditions, asset return volatility is estimated using GARCH-type models. The performance of this analytical approach is evaluated by comparing its numerical results with those obtained using alternative methods, such as Monte Carlo simulations and the conventional warrant valuation framework. An empirical analysis based on data from the Stock Exchange of Thailand indicates that the proposed method yields improved pricing accuracy with lower estimation errors than existing benchmarks. Full article
(This article belongs to the Section Probabilistic & Statistical Mathematics)
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19 pages, 3707 KB  
Article
ORAKULUM: An Information-Impact Asset Pricing Model Introducing a Jump-Diffusion Framework for Information-Driven Markets
by Zoltán Köntös and Ruszlan Megdetovics Rahimkulov
Risks 2026, 14(5), 108; https://doi.org/10.3390/risks14050108 - 6 May 2026
Viewed by 454
Abstract
Standard asset pricing models treat price dynamics as a stochastic process driven by undifferentiated random noise, rendering them agnostic about the primary engine of price discovery: the arrival of economically significant information. This paper introduces ORAKULUM, a structured Information-Impact Asset Pricing Model that [...] Read more.
Standard asset pricing models treat price dynamics as a stochastic process driven by undifferentiated random noise, rendering them agnostic about the primary engine of price discovery: the arrival of economically significant information. This paper introduces ORAKULUM, a structured Information-Impact Asset Pricing Model that reconceptualises the log-price as a signed information ledger. Each market-relevant event appends a weighted entry that either permanently revises the market consensus or temporarily disturbs it before decaying exponentially toward the new equilibrium. Mathematically, ORAKULUM is a jump-diffusion process combining a Wiener component for continuous micro-uncertainty with a Poisson-driven jump component for discrete macroeconomic and geopolitical shocks. The log-price identity xt=x0+μ·t+Ai+Bi·e(γtti)+σ·W(t) decomposes price dynamics into permanent and transient information impact, admits a natural event catalogue calibration, and supports Monte Carlo scenario simulation. We present the complete theoretical foundations, a closed-form expected path solution, a gradient-descent calibration procedure, and a fully documented Python3 reference implementation. An empirical illustration applies the model to XAU/USD and EUR/USD market data downloaded from Yahoo Finance, demonstrating ORAKULUM’s capacity to generate economically interpretable, real-time prediction clouds in response to central bank communications, inflation releases, and geopolitical shocks. Full article
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28 pages, 7358 KB  
Article
Determinants of Base Metal Prices: A Study Across Economic, Investment, and Monetary Drivers (2005–2017)
by Javier Petri, Luis Iglesias and Julián Alonso
Economies 2026, 14(5), 163; https://doi.org/10.3390/economies14050163 - 5 May 2026
Viewed by 630
Abstract
Estimating long-term prices for base metals is central to the financial viability of mining investments, yet prices remain highly volatile and difficult to forecast. This study systematizes the determinants of base metal prices and evaluates their empirical influence using daily and weekly data [...] Read more.
Estimating long-term prices for base metals is central to the financial viability of mining investments, yet prices remain highly volatile and difficult to forecast. This study systematizes the determinants of base metal prices and evaluates their empirical influence using daily and weekly data from the London Metal Exchange (LME) for aluminium, copper, nickel, and zinc between April 2005 and May 2017. In this context, the study aims to identify and evaluate the key economic, financial, and physical drivers of base metal prices, with particular emphasis on distinguishing between short-run predictive factors and long-run equilibrium determinants. After aligning metal prices with candidate explanatory variables, linear associations are quantified through Pearson correlations and alternative functional forms are explored for price modelling, including linear, log-linear, and selected nonlinear transformations. The methodology is complemented with econometric diagnostics. Explanatory variables are grouped into four categories: (i) supply–demand metrics (inventories, production–consumption balances, sales aggregates, and LME position data), (ii) business cycle and income proxies (global GDP growth, China Caixin PMI, the U.S. S&P 500 index, and China steel rebar futures), (iii) investment variables (cross-metal prices and Brent crude), and (iv) monetary indicators (U.S. and the U.S. 10-year yield). Results show that short-run price movements are mainly driven by business cycle indicators and inventory dynamics, while long-run trends reflect structural supply conditions. Monetary variables generate temporary price impulses, and prices tend to lead speculative positioning rather than the reverse. Full article
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31 pages, 3336 KB  
Article
Forecasting Peruvian Blueberry Exports for Sustainable Agricultural Trade Management: Markov Chains, SARIMA, and Log-Linear Growth
by Jean Michell Carrión-Mezones, Francisco Eduardo Cúneo-Fernández and Rogger Orlando Morán-Santamaría
Sustainability 2026, 18(9), 4529; https://doi.org/10.3390/su18094529 - 4 May 2026
Viewed by 1211
Abstract
Peruvian fresh blueberry exports have expanded rapidly since 2012, yet strong seasonality and price–volume fluctuations continue to complicate trade planning and export decision-making, thereby threatening the long-term economic sustainability of the sector. Using monthly series for 2012–2025, this study compares three forecasting approaches [...] Read more.
Peruvian fresh blueberry exports have expanded rapidly since 2012, yet strong seasonality and price–volume fluctuations continue to complicate trade planning and export decision-making, thereby threatening the long-term economic sustainability of the sector. Using monthly series for 2012–2025, this study compares three forecasting approaches to export value (FOB), export volume and unit price: (i) a seasonal Markov chain with Monte Carlo simulation (Markov–Monte Carlo), (ii) a log-linear growth model, and (iii) a seasonal ARIMA (SARIMA) model estimated using logarithmic data. The models are evaluated under a common train–test design, with the last 12 months (September 2024–August 2025) reserved for out-of-sample assessment. Model performance was evaluated through standard metrics, specifically Mean Absolute Error (MAE) and Root Mean Square Error (RMSE), while model adequacy was examined through residual diagnostics, including Ljung–Box tests. For the Markov–Monte Carlo approach, simulated distributions were also used to characterize forecast uncertainty. Findings indicate that the log-linear growth model provides the most accurate short-term point forecasts for FOB values, and the SARIMA model performs better for export volume; the Markov–Monte Carlo approach, however, yields the best performance for export prices and provides additional insights into seasonal regimes. Overall, these results suggest that no single model dominates across all dimensions of the export chain. Instead, the combined use of forecast approaches offers a more comprehensive basis for sustainable trade management, export planning, and risk management in dynamic agricultural export sectors. Full article
(This article belongs to the Special Issue Agricultural Economics and Sustainable Agricultural Food Value Chains)
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23 pages, 1745 KB  
Article
Landauer-Based Economic Temperature in Blockspace Markets: Evidence from Bitcoin and Ethereum
by Michael Zouari, Ilan Alon and Zeev Shtudiner
Entropy 2026, 28(5), 508; https://doi.org/10.3390/e28050508 - 1 May 2026
Viewed by 867
Abstract
The Landauer principle motivates the definition of economic temperature as the monetary price of processing a bit irreversibly. No empirical test of this definition exists in transparent fee markets. This paper fills that gap using daily Bitcoin and Ethereum data, constructing canonical thermodynamic [...] Read more.
The Landauer principle motivates the definition of economic temperature as the monetary price of processing a bit irreversibly. No empirical test of this definition exists in transparent fee markets. This paper fills that gap using daily Bitcoin and Ethereum data, constructing canonical thermodynamic state variables and evaluating five diagnostic layers: state variable behavior, Maxwell-type integrability, Carnot-style efficiency bounds, nonlinear regime separation, and structural break sensitivity to protocol events. Bitcoin’s log-temperature behaves as a persistent mean-reverting process with an AR(1) coefficient of 0.97 and a half-life of 21 days; Ethereum is highly persistent, with weaker formal evidence of stationarity than Bitcoin. Maxwell integrability is frequency-dependent: Bitcoin passes all four relations at monthly frequency, whereas Ethereum passes two of four. Carnot-style evidence is the strongest: realized fee extraction efficiency stays well below the implied bound, with daily compliance exceeding 97% on both chains. Structural breaks around Bitcoin ordinals, EIP-1559, the merge, and Shanghai confirm that protocol changes reorganize the temperature relation. The thermodynamic framework provides structure that standard fee market analysis does not, including a first principles efficiency bound and a state space coherence test. The findings provide partial, frequency-dependent, and chain-specific empirical support for a Landauer-based thermodynamic description of blockspace markets. Full article
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34 pages, 13121 KB  
Article
Mortality Forecasting Using LSTM-CNN Model
by Ning Zhang, Jingyang Chen, Hao Chen and Jingzhen Liu
Axioms 2026, 15(5), 324; https://doi.org/10.3390/axioms15050324 - 29 Apr 2026
Viewed by 342
Abstract
Accurate mortality prediction is essential to actuarial practice as it is directly linked to insurance pricing, reserving, and the management of longevity risk. This study proposes a deep neural network (DNN) model for the mortality rates of multiple populations; it is composed of [...] Read more.
Accurate mortality prediction is essential to actuarial practice as it is directly linked to insurance pricing, reserving, and the management of longevity risk. This study proposes a deep neural network (DNN) model for the mortality rates of multiple populations; it is composed of long short-term memory (LSTM) and convolutional neural network (CNN) components. As mortality trends evolve over long time horizons, and as capturing the complex dependencies among mortality rates across countries or regions with a linear model is challenging, the LSTM and CNN were applied to mortality modeling. The former can automatically learn long-term dependencies of sequential data, whereas the latter can extract local features from grid or sequential data. Formulated as a nonlinear generalization of the Lee–Carter decomposition, the model maps the log-mortality matrix logM to future logm(x,t) end-to-end and generates multi-step forecasts through dynamic recursive prediction. Then, the DNN and baseline models were used to fit mortality data of 21 countries from the Human Mortality Database (HMD), which were divided into training and test sets with the year 2000 as the split point. Extensive numerical experiments from the perspectives of accuracy, stability, and reliability of long-term forecasting revealed that DNN models yield better predictive performance, particularly the LSTM-CNN model. It combines the LSTM, CNN, and fully connected network (FCN) layers and thus exploits each deep neural network to fit nonlinear age, period, and cohort effects as well as their interactive terms to achieve better predictive performance. However, the CNN still outperformed other models for certain groups. In addition, the conclusions hold for remaining life expectancy. Full article
(This article belongs to the Special Issue Financial Mathematics and Econophysics)
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35 pages, 2050 KB  
Article
Leakage-Controlled Horizon-Specific Model Selection for Daily Equity Forecasting: An Automated Multi-Model Pipeline
by Francisco Augusto Nuñez Perez, Francisco Javier Aguilar Mosqueda, Adrian Ramos Cuevas, Jaqueline Muñoz Beltran and Jose Cruz Nuñez Perez
Forecasting 2026, 8(2), 34; https://doi.org/10.3390/forecast8020034 - 20 Apr 2026
Viewed by 936
Abstract
Short-horizon equity forecasting remains challenging because daily prices are noisy, heavy-tailed, and subject to structural breaks and regime shifts. We develop a fully automated, reproducible, and leakage-controlled multi-model pipeline for daily forecasting with horizon-specific configuration selection. The task is formulated as predicting cumulative [...] Read more.
Short-horizon equity forecasting remains challenging because daily prices are noisy, heavy-tailed, and subject to structural breaks and regime shifts. We develop a fully automated, reproducible, and leakage-controlled multi-model pipeline for daily forecasting with horizon-specific configuration selection. The task is formulated as predicting cumulative H-day log-returns from OHLCV-derived information and converting them to implied price forecasts. All model families share a homologated design: causal feature construction, a strictly chronological split with an explicit purging rule to prevent label-window overlap for multi-day targets, training-only robustification (winsorization and adaptive clipping), and a unified metric suite computed consistently in return and price spaces. The framework benchmarks transparent baselines (zero- and mean-return), gradient-boosted trees (XGBoost), and deep temporal models (LSTM and CNN/TCN). Lookback length L{60,180,500} is selected via an internal walk-forward procedure on the pre-evaluation block, and final performance is reported on an external hold-out segment (last 15% of instances). Experiments on daily data for MT, DELL, and the S&P 500 index (through 3 February 2026) show that all families achieve similarly strong price-level fit at H=1, largely driven by persistence in the price process, while separation across families becomes more visible at H=5. However, predictive performance in return space remains weak, with R2 close to zero or negative, and Diebold–Mariano tests do not provide consistent evidence of statistical superiority over naive benchmarks. Under an operational rule that minimizes hold-out RMSE on the price scale, selected models are asset- and horizon-dependent, supporting horizon-wise selection rather than a single global architecture. Overall, the primary contribution lies in the proposed leakage-controlled evaluation and benchmarking framework rather than in demonstrating consistent predictive gains in financial time series forecasting. Full article
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29 pages, 1375 KB  
Article
A Distribution-Free Neural Estimator for Mean Reversion, with Application to Energy Commodity Markets
by Carlo Mari and Emiliano Mari
Mathematics 2026, 14(8), 1302; https://doi.org/10.3390/math14081302 - 13 Apr 2026
Viewed by 341
Abstract
Accurate estimation of the mean-reversion speed α in the AR(1) process Xt+1=(1α)Xt+εt is central to energy-commodity modelling. Classical estimators such as GARCH, jump-diffusion, and regime-switching produce model-conditioned estimates by [...] Read more.
Accurate estimation of the mean-reversion speed α in the AR(1) process Xt+1=(1α)Xt+εt is central to energy-commodity modelling. Classical estimators such as GARCH, jump-diffusion, and regime-switching produce model-conditioned estimates by embedding α within distributional assumptions, so that different model choices yield different α^ values from the same series without a principled criterion to adjudicate. We propose a distribution-free neural estimator based on a Temporal Convolutional Network (TCN) trained on synthetic AR(1) series with Sinh-ArcSinh (SAS) innovations. Distribution-free here means that no parametric family is assumed for the innovation distribution at inference time: the estimator imposes no distributional hypothesis when processing a new series. The SAS family serves as a training vehicle—not a model for the real data—chosen for its ability to span a broad range of tail weights and asymmetry profiles. The theoretical foundation is spectral invariance: the Yule–Walker equations establish that the autocorrelation structure ρk=(1α)k depends on α alone, provided innovations are uncorrelated across lags—a condition satisfied not only by i.i.d. innovations but also by conditionally heteroscedastic processes such as GARCH. The TCN therefore generalises to volatility-clustering environments without modification, learning to extract α from temporal dependence alone, independently of the marginal innovation distribution and of the temporal variance structure. On held-out test series the estimator outperforms all classical competitors, with the advantage growing monotonically with non-Gaussianity. A robustness analysis on three out-of-distribution innovation families and on AR(1)-GARCH(1,1) processes empirically validates the spectral invariance guarantee across both marginal and temporal variance structure, including near-integrated GARCH processes where innovation kurtosis far exceeds the training range. The distribution-free α^ enables a two-stage pipeline in which α and the innovation distribution are characterised independently—a decoupling structurally impossible in classical likelihood-based approaches. Once trained, the TCN acts as a universal mean-reversion estimator applicable to any price series without re-fitting. Applied to four energy markets—Italian natural gas (PSV price), Italian electricity (PUN price), US Henry Hub, and US PJM West Hub—spanning log-return kurtosis from near-Gaussian to strongly heavy-tailed, the TCN yields robust, distribution-free estimates of mean-reversion speed. Full article
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13 pages, 2447 KB  
Data Descriptor
Electric Vehicle Routing with Time Windows and Heterogeneous Charging-Station Attribute Dataset
by Ayoub Hanif, Meryem Abid, Mohamed Tabaa, Hassna Bensag and Mohamed Youssfi
Data 2026, 11(4), 83; https://doi.org/10.3390/data11040083 - 12 Apr 2026
Viewed by 744
Abstract
This paper describes the benchmark dataset for the electric vehicle routing problem with time windows. It is designed to facilitate the large-scale and reproducible evaluation of routing approaches under diverse charging scenarios. It is an extension of the Homberger 1000-customer vehicle-routing benchmark dataset [...] Read more.
This paper describes the benchmark dataset for the electric vehicle routing problem with time windows. It is designed to facilitate the large-scale and reproducible evaluation of routing approaches under diverse charging scenarios. It is an extension of the Homberger 1000-customer vehicle-routing benchmark dataset through the incorporation of computationally derived charging-station data. For the 60 base instances included in the dataset, charging-station locations are randomly generated within the customer-coordinate bounds, and two variants are provided, resulting in 120 benchmark problems used in the validation and baseline analyses. A normalized local customer-density score is derived for each station. It is used to determine charging rates and log-normal parameters for prices and waiting times. Two variants are included in the dataset. Variant A maintains the original customer time-window constraints, while Variant B relaxes customer due dates based on the distance from the depot, subject to the depot closing time. The dataset is complemented by instance files, station attributes, parameters, and scripts. It also includes the results of feasibility tests, baseline solver tests, difficulty analyses, and sensitivity tests. These results show that the benchmark includes both easier and harder instance classes under different charging settings. Overall, the dataset is intended to support its use as a reproducible benchmark. Full article
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