Time Series Forecasting

Large language models (LLMs) are increasingly deployed in quantitative finance for stock price forecasting. This review synthesizes recent applications of LLMs in this domain, including extracting sentiment from financial news and social media, analyzing financial reports and earnings-call transcripts, tokenizing or symbolizing stock price series, and constructing multi-agent trading systems. Particular attention is paid to practical pitfalls that are often understated in the literature, such as fragility in sentiment analysis, dataset and horizon design, performance evaluation metrics, data leakage, illiquidity premia, and limits of stock price predictability. Organized from a hedge-fund perspective, the review is intended to guide both academic researchers and hedge fund managers in integrating LLMs into real-world trading pipelines and in stress-testing their robustness under realistic market frictions.

Accurate prediction of intersection turning movements is essential for adaptive signal control but remains difficult due to the high volatility of directional flows. This study proposes HFD-TM (Hierarchical Flow-Decomposition for Turning Movement Prediction), a hierarchical deep learning framework that predicts turning movements by first forecasting corridor through-movements and then expanding these predictions to individual turning streams. This design is motivated by empirical traffic structure, where corridor flows account for 65.1% of total volume, exhibit lower volatility than turning movements, and explain 35.5% of turning-movement variance. A physics-informed loss function enforces flow conservation to maintain structural consistency. Evaluated on six months of 15-minute interval LiDAR (Light Detection and Ranging) data from a six-intersection corridor in Nashville, Tennessee, HFD-TM achieves a mean absolute error of 2.49 vehicles per interval, reducing MAE by 5.7% compared to a Transformer and by 27.0% compared to a GRU (Gated Recurrent Unit). Ablation results show that hierarchical decomposition provides the largest performance gain, while training time is 12.8 times lower than DCRNN (Diffusion Convolutional Recurrent Neural Network), demonstrating suitability for real-time traffic applications.

Tabular foundation models, particularly Prior-data Fitted Networks like TabPFN have emerged as the leading contender in a myriad of tasks ranging from data imputation to label prediction on the tabular data format surpassing the historical successes of tree-based models. This has led to investigations on their applicability to forecasting time series data which can be formulated as a tabular problem. While recent work to this end has displayed positive results, most works have limited their treatment of multivariate time series problems to several independent univariate time series forecasting subproblems, thus ignoring any inter-channel interactions. Overcoming this limitation, we introduce a generally applicable framework for multivariate time series forecasting using tabular foundation models. We achieve this by recasting the multivariate time series forecasting problem as a series of scalar regression problems which can then be solved zero-shot by any tabular foundation model with regression capabilities. We present results of our method using the TabPFN-TS backbone and compare performance with the current state of the art tabular methods.

We present QARIMA, a quantum state-similarity-based reconstruction of the classical ARIMA modelling pipeline. Rather than using a quantum circuit as a standalone forecaster, QARIMA preserves ARIMA's interpretable forecasting structure while reformulating its core building blocks through analogous quantum-compatible modules. The framework integrates quantum differencing assessment, QACF/QPACF lag discovery, compact-swap-test state projection, swap-test/VQC-based AR and MA coefficient estimation, and weak-lag refinement within a single ARIMA forecasting workflow. QACF and QPACF serve the functional roles of ACF and PACF for MA and AR lag discovery, but construct lag relevance through quantum measurement geometry rather than direct classical correlation. Given screened candidate orders $(p,d,q)$, AR and MA coefficients are estimated through state-alignment losses incorporating cosine alignment, entropy regularization, phase correction, and norm control. We evaluate QARIMA across environmental, climatic, industrial, and weather time-series datasets using rolling-origin out-of-sample testing against automated classical ARIMA baselines, with performance assessed through MSE, MAPE, and Diebold--Mariano tests. The results show that quantum state-similarity modules can produce competitive and, in several cases, improved forecasting behaviour while preserving ARIMA's transparency, modularity, and interpretability. QARIMA therefore establishes a distinct pathway for quantum-enhanced statistical forecasting: its modules remain functionally analogous to classical ARIMA subroutines, but are not algebraic replicas; they serve the same modelling roles through state overlap, projection, and measurement-driven parameter estimation.

Industrial forecasting often involves multi-source asynchronous signals and multi-output targets, while deployment requires explicit trade-offs between prediction error and model complexity. Current practices typically fix alignment strategies or network designs, making it difficult to systematically co-design preprocessing, architecture, and hyperparameters in budget-limited training-based evaluations. To address this issue, we propose an auto-configuration framework that outputs a deployable Pareto set of forecasting models balancing error and complexity. At the model level, a Multi-Scale Bi-Branch Convolutional Neural Network (MS--BCNN) is developed, where short- and long-kernel branches capture local fluctuations and long-term trends, respectively, for multi-output regression. At the search level, we unify alignment operators, architectural choices, and training hyperparameters into a hierarchical-conditional mixed configuration space, and apply Player-based Hybrid Multi-Objective Evolutionary Algorithm (PHMOEA) to approximate the error--complexity Pareto frontier within a limited computational budget. Experiments on hierarchical synthetic benchmarks and a real-world sintering dataset demonstrate that our framework outperforms competitive baselines under the same budget and offers flexible deployment choices.

Passenger assistance services are essential for accessible rail travel, yet demand varies substantially across stations and over time, creating challenges for workforce planning and staff rostering. This paper presents a data-driven decision support framework for forecasting station-level passenger assistance demand and translating forecasts into workforce plans. The forecasting component applies a horizon-aware Prophet modelling approach using multi-source operational data, while the planning component maps demand forecasts to staffing requirements under service and operational constraints through an interpretable red-amber-green risk framework. The approach has been implemented within a production-grade system to support routine planning and staffing decisions across LNER-managed stations. Results demonstrate improved forecast accuracy relative to year-on-year baseline methods, with absolute error reduced by up to 76.9%, and show that forecast-informed staffing is associated with an approximate 50% reduction in failed passenger assistance deliveries attributable to staff availability. These findings highlight the value of integrating interpretable forecasting with operational work.

Heterogeneity in time series data is more pronounced than in vision or language, as temporal dynamics vary substantially across domains and tasks. Existing efforts on training time series foundation models (TSFMs) from scratch are often trained with mixed-batch strategies that merge large-scale datasets, which can cause gradient conflicts and degrade representation quality. To address this, we propose a fine-grained learning method that distills invariant knowledge from heterogeneous series while reducing cross-domain interference. We characterize heterogeneity at two levels: inter-domain and intra-domain. To tackle this bi-level heterogeneity, we design a federated learning method that mitigates intra-domain conflicts by enforcing domain-invariant and semantically consistent representations through local regularization, and addresses inter-domain discrepancies by enhancing cross-domain collaboration via domain-aware aggregation. Experiments across diverse benchmarks show that TSFMs trained with our method consistently outperform both centralized and federated TSFM baselines in point and probabilistic forecasting, while also achieving competitive zero-shot performance at scale, offering a flexible pathway for training TSFMs from scratch in heterogeneous environments.

Accurate forecasting of industrial time series requires balancing predictive accuracy with physical plausibility under non-stationary operating conditions. Existing data-driven models often achieve strong statistical performance but struggle to respect regime-dependent interaction structures and transport delays inherent in real-world systems. To address this challenge, we propose DSPR (Dual-Stream Physics-Residual Networks), a forecasting framework that explicitly decouples stable temporal patterns from regime-dependent residual dynamics. The first stream models the statistical temporal evolution of individual variables. The second stream focuses on residual dynamics through two key mechanisms: an Adaptive Window module that estimates flow-dependent transport delays, and a Physics-Guided Dynamic Graph that incorporates physical priors to learn time-varying interaction structures while suppressing spurious correlations. Experiments on four industrial benchmarks spanning heterogeneous regimes demonstrate that DSPR consistently improves forecasting accuracy and robustness under regime shifts while maintaining strong physical plausibility. It achieves state-of-the-art predictive performance, with Mean Conservation Accuracy exceeding 99% and Total Variation Ratio reaching up to 97.2%. Beyond forecasting, the learned interaction structures and adaptive lags provide interpretable insights that are consistent with known domain mechanisms, such as flow-dependent transport delays and wind-to-power scaling behaviors. These results suggest that architectural decoupling with physics-consistent inductive biases offers an effective path toward trustworthy industrial time-series forecasting. Furthermore, DSPR's demonstrated robust performance in long-term industrial deployment bridges the gap between advanced forecasting models and trustworthy autonomous control systems.

Understanding how training shapes the geometry of recurrent network dynamics is a central problem in time-series modeling. We study the emergence of low-dimensional dominant manifolds in the training of Reservoir Computing (RC) networks for temporal forecasting tasks. For a general linear continuous-time reservoir in the infinite-data limit, we show that the training data generate an invariant subspace of the trained reservoir, whose dimension equals the number of dominant modes. We then specialize to a simplified diagonal linear reservoir, where we link the dominant eigenvalues and eigenvectors to the spectrum of a backward Dynamic Mode Decomposition matrix, which yields a finite-dimensional approximation of the backward-time Koopman operator of the system generating the training data. We illustrate the emergence of these dominant modes during training in simulation, and discuss how the analysis may be extended to nonlinear RC via tangent dynamics and differential p-dominance.

Data-driven models for building thermal dynamics are a scalable approach for enabling energy-efficient operation through fault detection & diagnosis or advanced control. To obtain accurate models, measurement data from a target building spanning months to years are required. Transfer Learning (TL) mitigates this challenge by employing pretrained models based on single or multiple source buildings. General multi-source TL models promise to outperform single-source TL, but alternative multi-source modeling architectures remain to be explored, and evaluation on real-world data is missing. Moreover, time series foundation models (TSFM) have emerged as candidates for the best-performing general models. Hence, we conduct a first, comprehensive assessment of general modeling approaches for building thermal dynamics, including multi-source TL and TSFMs. Our assessment includes ablations using four state-of-the-art multi-source TL architectures and evaluations on synthetic as well as real-world data. We demonstrate that multi-source TL models are highly effective in accurately modeling buildings in real-world applications, yielding up to 63% lower forecasting errors compared to single-source TL. Moreover, our results suggest a trade-off between multi-source TL models exclusively pretrained with building data and TSFMs pretrained with a multitude of different time series, revealing that data from 16-32 source buildings must be available over 1 year for pretraining multi-source TL models to consistently outperform TSFMs as evaluated using the mean absolute error. These findings provide practical guidance for selecting modeling strategies based on the number of source buildings available for pretraining multi-source TL models.

Multivariate time series forecasting often struggles to capture long-range dependencies due to fixed lookback windows. Retrieval-augmented forecasting addresses this by retrieving historical segments from memory, but existing approaches rely on a channel-agnostic strategy that applies the same references to all variables. This neglects inter-variable heterogeneity, where different channels exhibit distinct periodicities and spectral profiles. We propose CRAFT (Channel-wise retrieval-augmented forecasting), a novel framework that performs retrieval independently for each channel. To ensure efficiency, CRAFT adopts a two-stage pipeline: a sparse relation graph constructed in the time domain prunes irrelevant candidates, and spectral similarity in the frequency domain ranks references, emphasizing dominant periodic components while suppressing noise. Experiments on seven public benchmarks demonstrate that CRAFT outperforms state-of-the-art forecasting baselines, achieving superior accuracy with practical inference efficiency.

Precision livestock farming requires accurate and timely heat stress prediction to ensure animal welfare and optimize farm management. This study presents a physics-informed digital twin (DT) framework combined with an uncertainty-aware, expert-weighted stacked ensemble for multimodal forecasting of Core Body Temperature (CBT) in dairy cattle. Using the high-frequency, heterogeneous MmCows dataset, the DT integrates an ordinary differential equation (ODE)-based thermoregulation model that simulates metabolic heat production and dissipation, a Gaussian process for capturing cow-specific deviations, a Kalman filter for aligning predictions with real-time sensor data, and a behavioral Markov chain that models activity-state transitions under varying environmental conditions. The DT outputs key physiological indicators, such as predicted CBT, heat stress probability, and behavioral state distributions are fused with raw sensor data and enriched through multi-scale temporal analysis and cross-modal feature engineering to form a comprehensive feature set. The predictive methodology is designed in a three-stage stacked ensemble, where stage 1 trains modality-specific LightGBM 'expert' models on distinct feature groups, stage 2 collects their predictions as meta-features, and at stage 3 Optuna-tuned LightGBM meta-model yields the final CBT forecast. Predictive uncertainty is quantified via bootstrapping and validated using Prediction Interval Coverage Probability (PICP). Ablation analysis confirms that incorporating DT-derived features and multimodal fusion substantially enhances performance. The proposed framework achieves a cross-validated R2 of 0.783, F1 score of 84.25% and PICP of 92.38% for 2-hour ahead forecasting, providing a robust, uncertainty-aware, and physically principled system for early heat stress detection and precision livestock management.

With the rise of time-of-use and tiered electricity pricing, energy consumers are encouraged to adopt peak-shifting strategies by automatically controlling high-power appliances. These help lower energy costs while enhancing the power grid's stability. To support such energy management with high resilience and responsiveness, reliable short-term load forecasting (STLF) plays a critical role. STLF predicts electricity consumption over time horizons ranging from minutes to days, using historical data, temporal patterns, and contextual factors. Traditional top-down forecasting methods struggle to capture the complex consumption patterns of diverse and mixed appliance loads. Although bottom-up methods improve forecasting accuracy by integrating appliance-level data, monitoring all appliances is costly, and many do not meaningfully impact total load prediction. Therefore, we propose GCA-BULF, a bottom-up short-term load forecasting framework based on grouped critical appliances, supported by three key designs. First, the Critical Appliance Filtering module ranks appliances according to their power consumption, switching frequency, and usage pattern periodicity, and identifies critical ones through iterative load decomposition. Next, the Related Appliance Grouping module clusters these appliances based on spatial and temporal correlations for group-level forecasting. Finally, the Collaborative Load Forecasting module refines the total load prediction by combining multiple group-level forecasts. We evaluate GCA-BULF on residential and office building load forecasting tasks. Experimental results reveal that GCA-BULF improves hourly total load forecasting by 20.85%-57.88% compared to existing top-down methods and by 33.03%-92.48% compared to bottom-up methods.

Dynamical systems describe how a physical system evolves over time. Physical processes can evolve faster or slower in different environmental conditions. We use time-warping as rescaling the time in a model of a physical system. This thesis proposes a new method of transfer learning for Recurrent Neural Networks (RNNs) based on time-warping. We prove that for a class of linear, first-order differential equations known as time lag models, an LSTM can approximate these systems with any desired accuracy, and the model can be time-warped while maintaining the approximation accuracy. The Time-Warping method of transfer learning is then evaluated in an applied problem on predicting fuel moisture content (FMC), an important concept in wildfire modeling. An RNN with LSTM recurrent layers is pretrained on fuels with a characteristic time scale of 10 hours, where there are large quantities of data available for training. The RNN is then modified with transfer learning to generate predictions for fuels with characteristic time scales of 1 hour, 100 hours, and 1000 hours. The Time-Warping method is evaluated against several known methods of transfer learning. The Time-Warping method produces predictions with an accuracy level comparable to the established methods, despite modifying only a small fraction of the parameters that the other methods modify.

Network analysis of inter-industry payment flows reveals structural economic relationships invisible to traditional bilateral measurement approaches, with significant implications for real-time economic monitoring. Analysing 532,346 UK payment records (2017--2024) across 89 industry sectors, we demonstrate that graph-theoretic features which include centrality measures and clustering coefficients improve payment flow forecasting by 8.8 percentage points beyond traditional time-series methods. Critically, network features prove most valuable during economic disruptions: during the COVID-19 pandemic, when traditional forecasting accuracy collapsed (R2} falling from 0.38 to 0.19), network-enhanced models maintained substantially better performance, with network contributions reaching +13.8 percentage points. The analysis identifies Financial Services, Wholesale Trade, and Professional Services as structurally central industries whose network positions indicate systemic importance beyond their transaction volumes. Network density increased 12.5% over the sample period, with visible disruption during 2020 followed by recovery exceeding pre-pandemic integration levels. These findings suggest payment network monitoring could enhance official statistics production by providing leading indicators of structural economic change and improving nowcasting accuracy during periods when traditional temporal patterns prove unreliable.

Although demand forecasting is a critical component of supply chain planning, actual retail data can exhibit irreconcilable seasonality, irregular spikes, and noise, rendering precise projections nearly unattainable. This paper proposes a three-step analytical framework that combines forecasting and operational analytics. The first stage consists of exploratory data analysis, where delivery-tracked data from 180,519 transactions are partitioned, and long-term trends, seasonality, and delivery-related attributes are examined. Secondly, the forecasting performance of a statistical time series decomposition model N-BEATS MSTL and a recent deep learning architecture N-HiTS were compared. N-BEATS and N-HiTS were both statistically, and hence were N-BEATS's and N-HiTS's statistically selected. Most recent time series deep learning models, N-HiTS, N-BEATS. N-HiTS and N-BEATS N-HiTS and N-HiTS outperformed the statistical benchmark to a large extent. N-BEATS was selected to be the most optimized model, as the one with the lowest forecasting error, in the 3rd and final stage forecasting values of the next 4 weeks of 1918 units, and provided those as a model with a set of deterministically integer linear program outcomes that are aimed to minimize the total delivery time with a set of bound budget, capacity, and service constraints. The solution allocation provided a feasible and cost-optimal shipping plan. Overall, the study provides a compelling example of the practical impact of precise forecasting and simple, highly interpretable model optimization in logistics.

Anticipating supply chain disruptions before they materialize is a core challenge for firms and policymakers alike. A key difficulty is learning to reason reliably about infrequent, high-impact events from noisy and unstructured inputs - a setting where general-purpose models struggle without task-specific adaptation. We introduce an end-to-end framework that trains LLMs to produce calibrated probabilistic forecasts using realized disruption outcomes as supervision. The resulting model substantially outperforms strong baselines - including GPT-5 - on accuracy, calibration, and precision. We also show that training induces more structured and reliable probabilistic reasoning without explicit prompting. These results suggest a general pathway for training domain-specific forecasting models that produce decision-ready signals. To support transparency we open-source the evaluation dataset used in this study. Dataset: https://huggingface.co/datasets/LightningRodLabs/supply-chain-predictions

This study examines the challenges of modeling complex and noisy data related to socioeconomic factors over time, with a focus on data from various districts in Odisha, India. Traditional time-series models struggle to capture both trends and variations together in this type of data. To tackle this, a Variational Neural Stochastic Differential Equation (V-NSDE) model is designed that combines the expressive dynamics of Neural SDEs with the generative capabilities of Variational Autoencoders (VAEs). This model uses an encoder and a decoder. The encoder takes the initial observations and district embeddings and translates them into a Gaussian distribution, which determines the mean and log-variance of the first latent state. Then the obtained latent state initiates the Neural SDE, which utilize neural networks to determine the drift and diffusion functions that govern continuous-time latent dynamics. These governing functions depend on the time index, latent state, and district embedding, which help the model learn the unique characteristics specific to each district. After that, using a probabilistic decoder, the observations are reconstructed from the latent trajectory. The decoder outputs a mean and log-variance for each time step, which follows the Gaussian likelihood. The Evidence Lower Bound (ELBO) training loss improves by adding a KL-divergence regularization term to the negative log-likelihood (nll). The obtained results demonstrate the effective learning of V-NSDE in recognizing complex patterns over time, yielding realistic outcomes that include clear trends and random fluctuations across different areas.

We study trajectory forecasting under squared loss for time series with weak conditional structure, using highly expressive prediction models. Building on the classical characterization of squared-loss risk minimization, we emphasize regimes in which the conditional expectation of future trajectories is effectively degenerate, leading to trivial Bayes-optimal predictors (flat for prices and zero for returns in standard financial settings). In this regime, increased model expressivity does not improve predictive accuracy but instead introduces spurious trajectory fluctuations around the optimal predictor. These fluctuations arise from the reuse of noise and result in increased prediction variance without any reduction in bias. This provides a process-level explanation for the degradation of Transformerbased forecasts on financial time series. We complement these theoretical results with numerical experiments on high-frequency EUR/USD exchange rate data, analyzing the distribution of trajectory-level forecasting errors. The results show that Transformer-based models yield larger errors than a simple linear benchmark on a large majority of forecasting windows, consistent with the variance-driven mechanism identified by the theory.

Time series forecasting is vital across many domains, yet existing models struggle with fixed-length inputs and inadequate multi-scale modeling. We propose MR-CDM, a framework combining hierarchical multi-resolution trend decomposition, an adaptive embedding mechanism for variable-length inputs, and a multi-scale conditional diffusion process. Evaluations on four real-world datasets demonstrate that MR-CDM significantly outperforms state-of-the-art baselines (e.g., CSDI, Informer), reducing MAE and RMSE by approximately 6-10 to a certain degree.

Livestock growth prediction is essential for optimising farm management and improving the efficiency and sustainability of livestock production, yet it remains underexplored due to limited large-scale datasets and privacy concerns surrounding farm-level data. Existing biophysical models rely on fixed formulations, while most machine learning approaches are trained on small, isolated datasets, limiting their robustness and generalisability. To address these challenges, we propose LivestockFL, the first federated learning framework specifically designed for livestock growth prediction. LivestockFL enables collaborative model training across distributed farms without sharing raw data, thereby preserving data privacy while alleviating data sparsity, particularly for farms with limited historical records. The framework employs a neural architecture based on a Gated Recurrent Unit combined with a multilayer perceptron to model temporal growth patterns from historical weight records and auxiliary features. We further introduce LivestockPFL, a novel personalised federated learning framework that extends the above federated learning framework with a personalized prediction head trained on each farm's local data, producing farm-specific predictors. Experiments on a real-world dataset demonstrate the effectiveness and practicality of the proposed approaches.

Test-time adaptation (TTA) enables neural forecasters to adapt to distribution shifts in streaming time series, but existing methods apply the same adaptation intensity regardless of the nature of the shift. We propose Regime-Guided Test-Time Adaptation (RG-TTA), a meta-controller that continuously modulates adaptation intensity based on distributional similarity to previously-seen regimes. Using an ensemble of Kolmogorov-Smirnov, Wasserstein-1, feature-distance, and variance-ratio metrics, RG-TTA computes a similarity score for each incoming batch and uses it to (i) smoothly scale the learning rate -- more aggressive for novel distributions, conservative for familiar ones -- and (ii) control gradient effort via loss-driven early stopping rather than fixed budgets, allowing the system to allocate exactly the effort each batch requires. As a supplementary mechanism, RG-TTA gates checkpoint reuse from a regime memory, loading stored specialist models only when they demonstrably outperform the current model (loss improvement >= 30%). RG-TTA is model-agnostic and strategy-composable: it wraps any forecaster exposing train/predict/save/load interfaces and enhances any gradient-based TTA method. We demonstrate three compositions -- RG-TTA, RG-EWC, and RG-DynaTTA -- and evaluate 6 update policies (3 baselines + 3 regime-guided variants) across 4 compact architectures (GRU, iTransformer, PatchTST, DLinear), 14 datasets (6 real-world multivariate benchmarks + 8 synthetic regime scenarios), and 4 forecast horizons (96, 192, 336, 720) under a streaming evaluation protocol with 3 random seeds (672 experiments total). Regime-guided policies achieve the lowest MSE in 156 of 224 seed-averaged experiments (69.6%), with RG-EWC winning 30.4% and RG-TTA winning 29.0%. Overall, RG-TTA reduces MSE by 5.7% vs TTA while running 5.5% faster; RG-EWC reduces MSE by 14.1% vs standalone EWC.

Forecasting multivariate time series remains challenging due to complex cross-variable dependencies and the presence of heterogeneous external influences. This paper presents Spectrogram-Enhanced Multimodal Fusion (SEMF), which combines spectral and temporal representations for more accurate and robust forecasting. The target time series is transformed into Morlet wavelet spectrograms, from which a Vision Transformer encoder extracts localized, frequency-aware features. In parallel, exogenous variables, such as financial indicators and macroeconomic signals, are encoded via a Transformer to capture temporal dependencies and multivariate dynamics. A bidirectional cross-attention module integrates these modalities into a unified representation that preserves distinct signal characteristics while modeling cross-modal correlations. Applied to multiple commodity price forecasting tasks, SEMF achieves consistent improvements over seven competitive baselines across multiple forecasting horizons and evaluation metrics. These results demonstrate the effectiveness of multimodal fusion and spectrogram-based encoding in capturing multi-scale patterns within complex financial time series.

Global AI weather forecasting still relies mainly on uniform-resolution models, making it hard to combine regional refinement, two-way regional-global coupling, and affordable training cost. We introduce StretchCast, a global-regional AI forecasting framework built on a variable-resolution stretched cubed-sphere (SCS) mesh that preserves a closed global domain while concentrating resolution over a target region. Within this framework, we develop a one-step predictor, SCS_Base Model, and a rollout-oriented multistep predictor, SCS_FCST4 Model, to test the feasibility of SCS-based forecasting and the benefit of joint multistep training. Experiments use ERA5 with 69 variables over 1998-2022. Because training compute remains limited, this study uses a coarse-resolution proof-of-concept configuration rather than a final high-resolution system. Even with only about 7,776 effective global grid cells and roughly 0.875 degree resolution over the center-refined face, the 23M-parameter SCS_Base Model yields stable multivariate forecasts. With 83M parameters and training cost on the order of hours, SCS_FCST4 Model delivers competitive medium-range anomaly-correlation evolution over the target region after unified reprojection, especially for geopotential height, specific humidity, and part of the lower-tropospheric winds, while maintaining smooth cross-face continuity and realistic multiscale structure in typhoon and spectral analyses. These results support StretchCast as a practical lightweight foundation for global-regional AI weather forecasting.

Forecasting is usually framed as a problem of model choice. This paper starts earlier, asking how much predictive information is available at each horizon. Under logarithmic loss, the answer is exact: the mutual information between the future observation and the declared information set equals the maximum achievable reduction in expected loss. This paper develops the consequences of that identity. Forecastability, defined as this mutual information evaluated across horizons, forms a profile whose shape reflects the dependence structure of the process and need not be monotone. Three structural properties are derived: compression of the information set can only reduce forecastability; the gap between the profile under a finite lag window and the full history gives an exact truncation error budget; and for processes with periodic dependence, the profile inherits the periodicity. Predictive loss decomposes into an irreducible component fixed by the information structure and an approximation component attributable to the method; their ratio defines the exploitation ratio, a normalised diagnostic for method adequacy. The exact equality is specific to log loss, but when forecastability is near zero, classical inequalities imply that no method under any loss can materially improve on the unconditional baseline. The framework provides a theoretical foundation for assessing, prior to any modelling, whether the declared information set contains sufficient predictive information at the horizon of interest.

Accurate short-term forecasting of agricultural commodity prices is critical for food security planning and smallholder income stabilisation in developing economies, yet machine-learning-ready datasets for this purpose remain scarce in South Asia. This paper makes two contributions. First, we introduce AgriPriceBD, a benchmark dataset of 1,779 daily retail mid-prices for five Bangladeshi commodities - garlic, chickpea, green chilli, cucumber, and sweet pumpkin - spanning July 2020 to June 2025, extracted from government reports via an LLM-assisted digitisation pipeline. Second, we evaluate seven forecasting approaches spanning classical models - naïve persistence, SARIMA, and Prophet - and deep learning architectures - BiLSTM, Transformer, Time2Vec-enhanced Transformer, and Informer - with Diebold-Mariano statistical significance tests. Commodity price forecastability is fundamentally heterogeneous: naïve persistence dominates on near-random-walk commodities. Time2Vec temporal encoding provides no statistically significant advantage over fixed sinusoidal encoding and causes catastrophic degradation on green chilli (+146.1% MAE, p<0.001). Prophet fails systematically, attributable to discrete step-function price dynamics incompatible with its smooth decomposition assumptions. Informer produces erratic predictions (variance up to 50x ground-truth), confirming sparse-attention Transformers require substantially larger training sets than small agricultural datasets provide. All code, models, and data are released publicly to support replication and future forecasting research on agricultural commodity markets in Bangladesh and similar developing economies.

Efficiently aggregating spatial or temporal horizons to acquire compact representations has become a unifying principle in modern deep learning models, yet learning data-adaptive representations for long-horizon sequence data, especially continuous sequences like time series, remains an open challenge. While fixed-size patching has improved scalability and performance, discovering variable-sized, data-driven patches end-to-end often forces models to rely on soft discretization, specific backbones, or heuristic rules. In this work, we propose Reinforcement Patching (ReinPatch), the first framework to jointly optimize a sequence patching policy and its downstream sequence backbone model using reinforcement learning. By formulating patch boundary placement as a discrete decision process optimized via Group Relative Policy Gradient (GRPG), ReinPatch bypasses the need for continuous relaxations and performs dynamic patching policy optimization in a natural manner. Moreover, our method allows strict enforcement of a desired compression rate, freeing the downstream backbone to scale efficiently, and naturally supports multi-level hierarchical modeling. We evaluate ReinPatch on time-series forecasting datasets, where it demonstrates compelling performance compared to state-of-the-art data-driven patching strategies. Furthermore, our detached design allows the patching module to be extracted as a standalone foundation patcher, providing the community with visual and empirical insights into the segmentation behaviors preferred by a purely performance-driven neural patching strategy.

Time series forecasting is critical across finance, healthcare, and cloud computing, yet progress is constrained by a fundamental bottleneck: the scarcity of large-scale, high-quality benchmarks. To address this gap, we introduce QuitoBench, a regime-balanced benchmark for time series forecasting with coverage across eight trend$\times$seasonality$\times$forecastability (TSF) regimes, designed to capture forecasting-relevant properties rather than application-defined domain labels. The benchmark is built upon Quito, a billion-scale time series corpus of application traffic from Alipay spanning nine business domains. Benchmarking 10 models from deep learning, foundation models, and statistical baselines across 232,200 evaluation instances, we report four key findings: (i) a context-length crossover where deep learning models lead at short context ($L=96$) but foundation models dominate at long context ($L \ge 576$); (ii) forecastability is the dominant difficulty driver, producing a $3.64 \times$ MAE gap across regimes; (iii) deep learning models match or surpass foundation models at $59 \times$ fewer parameters; and (iv) scaling the amount of training data provides substantially greater benefit than scaling model size for both model families. These findings are validated by strong cross-benchmark and cross-metric consistency. Our open-source release enables reproducible, regime-aware evaluation for time series forecasting research.

Accurate short-term air-quality forecasting is essential for public health protection and urban management, yet many recent forecasting frameworks rely on complex, data-intensive, and computationally demanding models. This study investigates whether lightweight and interpretable forecasting approaches can provide competitive performance for hourly PM2.5 prediction in Beijing, China. Using multi-year pollutant and meteorological time-series data, we developed a leakage-aware forecasting workflow that combined chronological data partitioning, preprocessing, feature selection, and exogenous-driver modeling under the Perfect Prognosis setting. Three forecasting families were evaluated: SARIMAX, Facebook Prophet, and NeuralProphet. To assess practical deployment behavior, the models were tested under two adaptive regimes: weekly walk-forward refitting and frozen forecasting with online residual correction. Results showed clear differences in both predictive accuracy and computational efficiency. Under walk-forward refitting, Facebook Prophet achieved the strongest completed performance, with an MAE of $37.61$ and an RMSE of $50.10$, while also requiring substantially less execution time than NeuralProphet. In the frozen-model regime, online residual correction improved Facebook Prophet and SARIMAX, with corrected SARIMAX yielding the lowest overall error (MAE $32.50$; RMSE $46.85$). NeuralProphet remained less accurate and less stable across both regimes, and residual correction did not improve its forecasts. Notably, corrected Facebook Prophet reached nearly the same error as its walk-forward counterpart while reducing runtime from $15$ min $21.91$ sec to $46.60$ sec. These findings show that lightweight additive forecasting strategies can remain highly competitive for urban air-quality prediction, offering a practical balance between accuracy, interpretability, ...

Accurate forecasting of future solar irradiance is essential for the effective control of solar thermal power plants. Although various kriging-based methods have been proposed to address the prediction problem, these methods typically do not provide an appropriate sampling strategy to dynamically position mobile sensors for optimizing prediction accuracy in real time, which is critical for achieving accurate forecasts with a minimal number of sensors. This paper introduces a dissimilarity map derived from a kriging model and proposes a persistent coverage control algorithm that effectively guides agents toward regions where additional observations are required to improve prediction performance. By means of experiments using mobile robots, the proposed approach was shown to obtain more accurate predictions than the considered baselines under various emulated irradiance fields.