Time Series Forecasting

Data normalization is a crucial component of deep learning models, yet its role in time series forecasting remains insufficiently understood. In this paper, we identify three central challenges for normalization in time series forecasting: temporal input distribution shift, spatial input distribution shift, and conditional output distribution shift. In this context, we revisit the widely used Reversible Instance Normalization (RevIN), by showing through ablation studies that several of its components are redundant or even detrimental. Based on these observations, we draw new perspectives to improve RevIN's robustness and generalization.

Forecasting crude oil prices remains challenging because market-relevant information is embedded in large volumes of unstructured news and is not fully captured by traditional polarity-based sentiment measures. This paper examines whether multi-dimensional sentiment signals extracted by large language models improve the prediction of weekly WTI crude oil futures returns. Using energy-sector news articles from 2020 to 2025, we construct five sentiment dimensions covering relevance, polarity, intensity, uncertainty, and forwardness based on GPT-4o, Llama 3.2-3b, and two benchmark models, FinBERT and AlphaVantage. We aggregate article-level signals to the weekly level and evaluate their predictive performance in a classification framework. The best results are achieved by combining GPT-4o and FinBERT, suggesting that LLM-based and conventional financial sentiment models provide complementary predictive information. SHAP analysis further shows that intensity- and uncertainty-related features are among the most important predictors, indicating that the predictive value of news sentiment extends beyond simple polarity. Overall, the results suggest that multi-dimensional LLM-based sentiment measures can improve commodity return forecasting and support energy-market risk monitoring.

Transformer-based time series foundation models face a fundamental trade-off in choice of tokenization: point-wise embeddings preserve temporal fidelity but scale poorly with sequence length, whereas fixed-length patching improves efficiency by imposing uniform boundaries that may disrupt natural transitions and blur informative local dynamics. In order to address these limitations, we introduce TimeSqueeze, a dynamic patching mechanism that adaptively selects patch boundaries within each sequence based on local signal complexity. TimeSqueeze first applies a lightweight state-space encoder to extract full-resolution point-wise features, then performs content-aware segmentation by allocating short patches to information-dense regions and long patches to smooth or redundant segments. This variable-resolution compression preserves critical temporal structure while substantially reducing the token sequence presented to the Transformer backbone. Specifically for large-scale pretraining, TimeSqueeze attains up to 20x faster convergence and 8x higher data efficiency compared to equivalent point-token baselines. Experiments across long-horizon forecasting benchmarks show that TimeSqueeze consistently outperforms comparable architectures that use either point-wise tokenization or fixed-size patching.

Mining time-frequency features is critical for time series forecasting. Existing research has predominantly focused on modeling low-frequency patterns, where most time series energy is concentrated. The overlooking of mid to high frequency continues to limit further performance gains in deep learning models. We propose FreqCycle, a novel framework integrating: (i) a Filter-Enhanced Cycle Forecasting (FECF) module to extract low-frequency features by explicitly learning shared periodic patterns in the time domain, and (ii) a Segmented Frequency-domain Pattern Learning (SFPL) module to enhance mid to high frequency energy proportion via learnable filters and adaptive weighting. Furthermore, time series data often exhibit coupled multi-periodicity, such as intertwined weekly and daily cycles. To address coupled multi-periodicity as well as long lookback window challenges, we extend FreqCycle hierarchically into MFreqCycle, which decouples nested periodic features through cross-scale interactions. Extensive experiments on seven diverse domain benchmarks demonstrate that FreqCycle achieves state-of-the-art accuracy while maintaining faster inference speeds, striking an optimal balance between performance and efficiency.

Time series foundation models (TSFMs) are increasingly deployed in high-stakes domains, yet their internal representations remain opaque. We present the first application of sparse autoencoders (SAEs) to a TSFM, training TopK SAEs on activations of Chronos-T5-Large (710M parameters) across six layers. Through 392 single-feature ablation experiments, we establish that every ablated feature produces a positive CRPS degradation, confirming causal relevance. Our analysis reveals a depth-dependent hierarchy: early encoder layers encode low-level frequency features, the mid-encoder concentrates causally critical change-detection features, and the final encoder compresses a rich but less causally important taxonomy of temporal concepts. The most critical features reside in the mid-encoder (max single-feature Delta CRPS = 38.61), not in the semantically richest final encoder layer, where progressive ablation paradoxically improves forecast quality. These findings demonstrate that mechanistic interpretability transfers effectively to TSFMs and that Chronos-T5 relies on abrupt-dynamics detection rather than periodic pattern recognition.

By capturing the prevailing sentiment and market mood, textual data has become increasingly vital for forecasting commodity prices, particularly in metal markets. However, the effectiveness of lightweight, finetuned large language models (LLMs) in extracting predictive signals for aluminum prices, and the specific market conditions under which these signals are most informative, remains under-explored. This study generates monthly sentiment scores from English and Chinese news headlines (Reuters, Dow Jones Newswires, and China News Service) and integrates them with traditional tabular data, including base metal indices, exchange rates, inflation rates, and energy prices. We evaluate the predictive performance and economic utility of these models through long-short simulations on the Shanghai Metal Exchange from 2007 to 2024. Our results demonstrate that during periods of high volatility, Long Short-Term Memory (LSTM) models incorporating sentiment data from a finetuned Qwen3 model (Sharpe ratio 1.04) significantly outperform baseline models using tabular data alone (Sharpe ratio 0.23). Subsequent analysis elucidates the nuanced roles of news sources, topics, and event types in aluminum price forecasting.

Online Time Series Forecasting (OTSF) requires models to continuously adapt to concept drift. However, existing methods often treat concept drift as a monolithic phenomenon. To address this limitation, we first redefine concept drift by categorizing it into two distinct types: Recurring Drift, where previously seen patterns reappear, and Emergent Drift, where entirely new patterns emerge. We then propose DynaME (Dynamic Multi-period Experts), a novel hybrid framework designed to effectively address this dual nature of drift. For Recurring Drift, DynaME employs a committee of specialized experts that are dynamically fitted to the most relevant historical periodic patterns at each time step. For Emergent Drift, the framework detects high-uncertainty scenarios and shifts reliance to a stable, general expert. Extensive experiments on several benchmark datasets and backbones demonstrate that DynaME effectively adapts to both concept drifts and significantly outperforms existing baselines.

Recent advances in time-series forecasting increasingly rely on pre-trained foundation-style models. While these models often claim broad generalization, existing evaluation protocols provide limited evidence. Indeed, most current benchmarks use static train-test splits that can easily lead to contamination as foundation models can inadvertently train on test data or perform model selection using test scores, which can inflate performance. We introduce Impermanent, a live benchmark that evaluates forecasting models under open-world temporal change by scoring forecasts sequentially over time on continuously updated data streams, enabling the study of temporal robustness, distributional shift, and performance stability rather than one-off accuracy on a frozen test set. Impermanent is instantiated on GitHub open-source activity, providing a naturally live and highly non-stationary dataset shaped by releases, shifting contributor behavior, platform/tooling changes, and external events. We focus on the top 400 repositories by star count and construct time series from issues opened, pull requests opened, push events, and new stargazers, evaluated over a rolling window with daily updates, alongside standardized protocols and leaderboards for reproducible, ongoing comparison. By shifting evaluation from static accuracy to sustained performance, Impermanent takes a concrete step toward assessing when and whether foundation-level generalization in time-series forecasting can be meaningfully claimed. Code and a live dashboard are available at https://github.com/TimeCopilot/impermanent and https://impermanent.timecopilot.dev.

Long-term time series forecasting (LTSF) is widely recognized as a central challenge in data mining and machine learning. LTSF has increasingly evolved into a benchmark-driven ''GAME,'' where models are ranked, compared, and declared state-of-the-art based primarily on marginal reductions in aggregated pointwise error metrics such as MSE and MAE. Across a small set of canonical datasets and fixed forecasting horizons, progress is communicated through leaderboard-style tables in which lower numerical scores define success. In this GAME, what is measured becomes what is optimized, and incremental error reduction becomes the dominant currency of advancement. We argue that this metric-centric regime is not merely incomplete, but structurally misaligned with the broader objectives of forecasting. In real-world settings, forecasting often prioritizes preserving temporal structure, trend stability, seasonal coherence, robustness to regime shifts, and supporting downstream decision processes. Optimizing aggregate pointwise error does not necessarily imply modeling these structural properties. As a result, leaderboard improvement may increasingly reflect specialization in benchmark configurations rather than a deeper understanding of temporal dynamics. This paper revisits LTSF evaluation as a foundational question in data science: what does it mean to measure forecasting progress? We propose a multi-dimensional evaluation perspective that integrates statistical fidelity, structural coherence, and decision-level relevance. By challenging the current metric monoculture, we aim to redirect attention from winning benchmark tables toward advancing meaningful, context-aware forecasting.

Forecasting physiological signals can support proactive monitoring and timely clinical intervention by anticipating critical changes in patient status. In this work, we address multivariate multi-horizon forecasting of physiological time series by jointly predicting heart rate, oxygen saturation, pulse rate, and respiratory rate at forecasting horizons of 15, 30, and 60 seconds. We propose a hybrid quantum-classical architecture that integrates a Variational Quantum Circuit (VQC) within a recurrent neural backbone. A GRU encoder summarizes the historical observation window into a latent representation, which is then projected into quantum angles used to parameterize the VQC. The quantum layer acts as a learnable non-linear feature mixer, modeling cross-variable interactions before the final prediction stage. We evaluate the proposed approach on the BIDMC PPG and Respiration dataset under a Leave-One-Patient-Out protocol. The results show competitive accuracy compared with classical and deep learning baselines, together with greater robustness to noise and missing inputs. These findings suggest that hybrid quantum layers can provide useful inductive biases for physiological time series forecasting in small-cohort clinical settings. The code is available at https://github.com/arco-group/quantum-ml.

Functional magnetic resonance imaging (fMRI) enables noninvasive investigation of brain function, while short clinical scan durations, arising from human and non-human factors, usually lead to reduced data quality and limited statistical power for neuroimaging research. In this paper, we propose BrainCast, a novel spatio-temporal forecasting framework specifically tailored for whole-brain fMRI time series forecasting, to extend informative fMRI time series without additional data acquisition. It formulates fMRI time series forecasting as a multivariate time series prediction task and jointly models temporal dynamics within regions of interest (ROIs) and spatial interactions across ROIs. Specifically, BrainCast integrates a Spatial Interaction Awareness module to characterize inter-ROI dependencies via embedding every ROI time series as a token, a Temporal Feature Refinement module to capture intrinsic neural dynamics within each ROI by enhancing both low- and high-energy temporal components of fMRI time series at the ROI level, and a Spatio-temporal Pattern Alignment module to combine spatial and temporal representations for producing informative whole-brain features. Experimental results on resting-state and task fMRI datasets from the Human Connectome Project demonstrate the superiority of BrainCast over state-of-the-art time series forecasting baselines. Moreover, fMRI time series extended by BrainCast improve downstream cognitive ability prediction, highlighting the clinical and neuroscientific impact brought by whole-brain fMRI time series forecasting in scenarios with restricted scan durations.

Exogenous variables offer valuable supplementary information for predicting future endogenous variables. Forecasting with exogenous variables needs to consider both past-to-future dependencies (i.e., temporal correlations) and the influence of exogenous variables on endogenous variables (i.e., channel correlations). This is pivotal when future exogenous variables are available, because they may directly affect the future endogenous variables. Many methods have been proposed for time series forecasting with exogenous variables, focusing on modeling temporal and channel correlations. However, most of them use a two-step strategy, modeling temporal and channel correlations separately, which limits their ability to capture joint correlations across time and channels. Furthermore, in real-world scenarios, time series are frequently affected by various forms of noises, underscoring the critical importance of robustness in such correlations modeling. To address these limitations, we propose GCGNet, a Graph-Consistent Generative Network for time series forecasting with exogenous variables. Specifically, GCGNet first employs a Variational Generator to produce coarse predictions. A Graph Structure Aligner then further guides it by evaluating the consistency between the generated and true correlations, where the correlations are represented as graphs, and are robust to noises. Finally, a Graph Refiner is proposed to refine the predictions to prevent degeneration and improve accuracy. Extensive experiments on 12 real-world datasets demonstrate that GCGNet outperforms state-of-the-art baselines.

Financial time-series forecasting is a high-stakes problem where regime shifts and shocks make point-accurate yet overconfident models dangerous. We propose Uncertainty-Gated Generative Modeling (UGGM), which treats uncertainty as an internal control signal that gates (i) representation via gated reparameterization, (ii) propagation via similarity and confidence routing, and (iii) generation via uncertainty-controlled predictive distributions, together with uncertainty-driven regularization and calibration to curb miscalibration. Instantiated on Weak Innovation AutoEncoder (WIAE-GPF), our UG-WIAE-GPF significantly improves risk-sensitive forecasting, delivering a 63.5% MSE reduction on NYISO (0.3508 $\rightarrow$ 0.1281), with improved robustness under shock intervals (mSE: 0.2739 $\rightarrow$ 0.1748).

Accurate analysis of industrial time-series big data is critical for the Prognostics and Health Management (PHM) of industrial equipment. While recent advancements in Large Language Models (LLMs) have shown promise in time-series analysis, existing methods typically focus on single-modality adaptations, failing to exploit the complementary nature of temporal signals, frequency-domain visual representations, and textual knowledge information. In this paper, we propose TS-MLLM, a unified multi-modal large language model framework designed to jointly model temporal signals, frequency-domain images, and textual domain knowledge. Specifically, we first develop an Industrial time-series Patch Modeling branch to capture long-range temporal dynamics. To integrate cross-modal priors, we introduce a Spectrum-aware Vision-Language Model Adaptation (SVLMA) mechanism that enables the model to internalize frequency-domain patterns and semantic context. Furthermore, a Temporal-centric Multi-modal Attention Fusion (TMAF) mechanism is designed to actively retrieve relevant visual and textual cues using temporal features as queries, ensuring deep cross-modal alignment. Extensive experiments on multiple industrial benchmarks demonstrate that TS-MLLM significantly outperforms state-of-the-art methods, particularly in few-shot and complex scenarios. The results validate our framework's superior robustness, efficiency, and generalization capabilities for industrial time-series prediction.

Chaotic time series are notoriously difficult to forecast. Small uncertainties in initial conditions amplify rapidly, while strong nonlinearities and regime dependent variability constrain predictability. Although modern deep learning often delivers strong short horizon accuracy, its black box nature limits scientific insight and practical trust in settings where understanding the underlying dynamics matters. To address this gap, we propose two complementary symbolic forecasters that learn explicit, interpretable algebraic equations from chaotic time series data. Symbolic Neural Forecaster (SyNF) adapts a neural network based equation learning architecture to the forecasting setting, enabling fully differentiable discovery of compact and interpretable algebraic relations. The Symbolic Tree Forecaster (SyTF) builds on evolutionary symbolic regression to search directly over equation structures under a principled accuracy complexity trade off. We evaluate both approaches in a rolling window nowcasting setting with one step ahead forecasting using several accuracy metrics and compare against a broad suite of baselines spanning classical statistical models, tree ensembles, and modern deep learning architectures. Numerical experiments cover a benchmark of 132 low dimensional chaotic attractors and two real world chaotic time series, namely weekly dengue incidence in San Juan and the Nino 3.4 sea surface temperature index. Across datasets, symbolic forecasters achieve competitive one step ahead accuracy while providing transparent equations that reveal salient aspects of the underlying dynamics.

Hierarchical time-series forecasting is essential for demand prediction across various industries. While machine learning models have obtained significant accuracy and scalability on such forecasting tasks, the interpretability of their predictions, informed by application, is still largely unexplored. To bridge this gap, we introduce a novel interpretability method for large hierarchical probabilistic time-series forecasting, adapting generic interpretability techniques while addressing challenges associated with hierarchical structures and uncertainty. Our approach offers valuable interpretative insights in response to real-world industrial supply chain scenarios, including 1) the significance of various time-series within the hierarchy and external variables at specific time points, 2) the impact of different variables on forecast uncertainty, and 3) explanations for forecast changes in response to modifications in the training dataset. To evaluate the explainability method, we generate semi-synthetic datasets based on real-world scenarios of explaining hierarchical demands for over ten thousand products at a large chemical company. The experiments showed that our explainability method successfully explained state-of-the-art industrial forecasting methods with significantly higher explainability accuracy. Furthermore, we provide multiple real-world case studies that show the efficacy of our approach in identifying important patterns and explanations that help stakeholders better understand the forecasts. Additionally, our method facilitates the identification of key drivers behind forecasted demand, enabling more informed decision-making and strategic planning. Our approach helps build trust and confidence among users, ultimately leading to better adoption and utilization of hierarchical forecasting models in practice.

Stock market prediction presents considerable challenges for investors, financial institutions, and policymakers operating in complex market environments characterized by noise, non-stationarity, and behavioral dynamics. Traditional forecasting methods, including fundamental analysis and technical indicators, often fail to capture the intricate patterns and cross-sectional dependencies inherent in financial markets. This paper presents an integrated framework combining a node transformer architecture with BERT-based sentiment analysis for stock price forecasting. The proposed model represents the stock market as a graph structure where individual stocks form nodes and edges capture relationships including sectoral affiliations, correlated price movements, and supply chain connections. A fine-tuned BERT model extracts sentiment information from social media posts and combines it with quantitative market features through attention-based fusion mechanisms. The node transformer processes historical market data while capturing both temporal evolution and cross-sectional dependencies among stocks. Experiments conducted on 20 S&P 500 stocks spanning January 1982 to March 2025 demonstrate that the integrated model achieves a mean absolute percentage error (MAPE) of 0.80% for one-day-ahead predictions, compared to 1.20% for ARIMA and 1.00% for LSTM. The inclusion of sentiment analysis reduces prediction error by 10% overall and 25% during earnings announcements, while the graph-based architecture contributes an additional 15% improvement by capturing inter-stock dependencies. Directional accuracy reaches 65% for one-day forecasts. Statistical validation through paired t-tests confirms the significance of these improvements (p < 0.05 for all comparisons). The model maintains lower error during high-volatility periods, achieving MAPE of 1.50% while baseline models range from 1.60% to 2.10%.

Time series forecasting has witnessed an increasing demand across diverse industrial applications, where accurate predictions are pivotal for informed decision-making. Beyond numerical time series data, reliable forecasting in practical scenarios requires integrating diverse exogenous factors. Such exogenous information is often multi-dimensional or even multimodal, introducing heterogeneous interactions that unimodal time series models struggle to capture. In this paper, we delve into an aviation maintenance scenario and identify three distinct types of exogenous factors that influence temporal dynamics through distinct interaction modes. Based on this empirical insight, we propose Aura, a universal framework that explicitly organizes and encodes heterogeneous external information according to its interaction mode with the target time series. Specifically, Aura utilizes a tailored tripartite encoding mechanism to embed heterogeneous features into well-established time series models, ensuring seamless integration of non-sequential context. Extensive experiments on a large-scale, three-year industrial dataset from China Southern Airlines, covering the Boeing 777 and Airbus A320 fleets, demonstrate that Aura consistently achieves state-of-the-art performance across all baselines and exhibits superior adaptability. Our findings highlight Aura's potential as a general-purpose enhancement for aviation safety and reliability.

While RAG has greatly enhanced LLMs, extending this paradigm to Time-Series Foundation Models (TSFMs) remains a challenge. This is exemplified in the Predictive Maintenance of the Pressure Regulating and Shut-Off Valve (PRSOV), a high-stakes industrial scenario characterized by (1) data scarcity, (2) short transient sequences, and (3) covariate coupled dynamics. Unfortunately, existing time-series RAG approaches predominantly rely on generated static vector embeddings and learnable context augmenters, which may fail to distinguish similar regimes in such scarce, transient, and covariate coupled scenarios. To address these limitations, we propose RAG4CTS, a regime-aware, training-free RAG framework for Covariate Time-Series. Specifically, we construct a hierarchal time-series native knowledge base to enable lossless storage and physics-informed retrieval of raw historical regimes. We design a two-stage bi-weighted retrieval mechanism that aligns historical trends through point-wise and multivariate similarities. For context augmentation, we introduce an agent-driven strategy to dynamically optimize context in a self-supervised manner. Extensive experiments on PRSOV demonstrate that our framework significantly outperforms state-of-the-art baselines in prediction accuracy. The proposed system is deployed in Apache IoTDB within China Southern Airlines. Since deployment, our method has successfully identified one PRSOV fault in two months with zero false alarm.

Accurate time series forecasting underpins decision-making in many domains, yetconventional ML development often faces data scarcity, distribution shift, anddiminishing returns from manual iteration. We propose Self-Evolving Agent forTime Series Algorithms (SEATS), a framework that autonomously generates, val-idates, and optimizes forecasting algorithm code through an iterative self-evolutionloop. Our design combines three mechanisms: (1) Metric-Advantage MCTS(MA-MCTS), which replaces fixed rewards with a statistically normalized advan-tage score for search guidance, (2) code review with running prompt refinement,so every successfully executed solution is reviewed and the running prompt encodescorrective patterns for later iterations, and (3) global steerable reasoning, whichcompares each evaluated node to global best- and worst-performing solutions forcross-trajectory transfer. A MAP-Elites archive maintains architectural diversity.Across four datasets and two metrics, SEATS wins seven of eight comparisonsagainst strong baselines TimeMixer, Timer, and SEMixer

We introduce Timer-S1, a strong Mixture-of-Experts (MoE) time series foundation model with 8.3B total parameters, 0.75B activated parameters for each token, and a context length of 11.5K. To overcome the scalability bottleneck in existing pre-trained time series foundation models, we perform Serial Scaling in three dimensions: model architecture, dataset, and training pipeline. Timer-S1 integrates sparse TimeMoE blocks and generic TimeSTP blocks for Serial-Token Prediction (STP), a generic training objective that adheres to the serial nature of forecasting. The proposed paradigm introduces serial computations to improve long-term predictions while avoiding costly rolling-style inference and pronounced error accumulation in the standard next-token prediction. Pursuing a high-quality and unbiased training dataset, we curate TimeBench, a corpus with one trillion time points, and apply meticulous data augmentation to mitigate predictive bias. We further pioneer a post-training stage, including continued pre-training and long-context extension, to enhance short-term and long-context performance. Evaluated on the large-scale GIFT-Eval leaderboard, Timer-S1 achieves state-of-the-art forecasting performance, attaining the best MASE and CRPS scores as a pre-trained model. Timer-S1 is released to facilitate further research.

The discovery rate of optical transients will explode to 10 million public alerts per night once the Vera C. Rubin Observatory's Legacy Survey of Space and Time comes online, overwhelming the traditional physics-based inference pipelines. A continuous-time forecasting AI model is of interest because it can deliver millisecond-scale inference for thousands of objects per day, whereas legacy MCMC codes need hours per object. In this paper, we propose SELDON, a new continuous-time variational autoencoder for panels of sparse and irregularly time-sampled (gappy) astrophysical light curves that are nonstationary, heteroscedastic, and inherently dependent. SELDON combines a masked GRU-ODE encoder with a latent neural ODE propagator and an interpretable Gaussian-basis decoder. The encoder learns to summarize panels of imbalanced and correlated data even when only a handful of points are observed. The neural ODE then integrates this hidden state forward in continuous time, extrapolating to future unseen epochs. This extrapolated time series is further encoded by deep sets to a latent distribution that is decoded to a weighted sum of Gaussian basis functions, the parameters of which are physically meaningful. Such parameters (e.g., rise time, decay rate, peak flux) directly drive downstream prioritization of spectroscopic follow-up for astrophysical surveys. Beyond astronomy, the architecture of SELDON offers a generic recipe for interpretable and continuous-time sequence modeling in any time domain where data are multivariate, sparse, heteroscedastic, and irregularly spaced.

Time series forecasting, which predicts future values from past observations, plays a central role in many domains and has driven the development of highly accurate neural network models. However, the complexity of these models often limits human understanding of the rationale behind their predictions. We propose PatchDecomp, a neural network-based time series forecasting method that achieves both high accuracy and interpretability. PatchDecomp divides input time series into subsequences (patches) and generates predictions by aggregating the contributions of each patch. This enables clear attribution of each patch, including those from exogenous variables, to the final prediction. Experiments on multiple benchmark datasets demonstrate that PatchDecomp provides predictive performance comparable to recent forecasting methods. Furthermore, we show that the model's explanations not only influence predicted values quantitatively but also offer qualitative interpretability through visualization of patch-wise contributions.

Time Series forecasting (TSF) in the modern era faces significant computational and storage cost challenges due to the massive scale of real-world data. Dataset Distillation (DD), a paradigm that synthesizes a small, compact dataset to achieve training performance comparable to that of the original dataset, has emerged as a promising solution. However, conventional DD methods are not tailored for time series and suffer from architectural overfitting and limited scalability. To address these issues, we propose Harmonic Dataset Distillation for Time Series Forecasting (HDT). HDT decomposes the time series into its sinusoidal basis through the FFT and aligns the core periodic structure by Harmonic Matching. Since this process operates in the frequency domain, all updates during distillation are applied globally without disrupting temporal dependencies of time series. Extensive experiments demonstrate that HDT achieves strong cross-architecture generalization and scalability, validating its practicality for large-scale, real-world applications.

Time series forecasters are widely used across various domains. Among them, MLP (multi-layer perceptron)-based forecasters have been proven to be more robust to noise compared to Transformer-based forecasters. However, MLP struggles to capture complex features, resulting in limitations on capturing long-range dependencies. To address this challenge, we propose XLinear, an MLP-based forecaster for long-range forecasting. Firstly, we decompose the time series into trend and seasonal components. For the trend component which contains long-range characteristics, we design Enhanced Frequency Attention (EFA) to capture long-term dependencies by leveraging frequency-domain operations. Additionally, a CrossFilter Block is proposed for the seasonal component to maintain the model's robustness to noise, avoiding the problems of low robustness often caused by attention mechanisms. Experimental results demonstrate that XLinear achieves state-of-the-art performance on test datasets. While keeping the lightweight architecture and high robustness of MLP-based models, our forecaster outperforms other MLP-based forecasters in capturing long-range dependencies.

Time series forecasting enables early warning and has driven asset performance management from traditional planned maintenance to predictive maintenance. However, the lack of interpretability in forecasting methods undermines users' trust and complicates debugging for developers. Consequently, interpretable time-series forecasting has attracted increasing research attention. Nevertheless, existing methods suffer from several limitations, including insufficient modeling of temporal dependencies, lack of feature-level interpretability to support early warning, and difficulty in simultaneously achieving the accuracy and interpretability. This paper proposes the interpretable polynomial learning (IPL) method, which integrates interpretability into the model structure by explicitly modeling original features and their interactions of arbitrary order through polynomial representations. This design preserves temporal dependencies, provides feature-level interpretability, and offers a flexible trade-off between prediction accuracy and interpretability by adjusting the polynomial degree. We evaluate IPL on simulated and Bitcoin price data, showing that it achieves high prediction accuracy with superior interpretability compared with widely used explainability methods. Experiments on field-collected antenna data further demonstrate that IPL yields simpler and more efficient early warning mechanisms.

The financial domain involves a variety of important time-series problems. Recently, time-series analysis methods that jointly leverage textual and numerical information have gained increasing attention. Accordingly, numerous efforts have been made to construct text-paired time-series datasets in the financial domain. However, financial markets are characterized by complex interdependencies, in which a company's stock price is influenced not only by company-specific events but also by events in other companies and broader macroeconomic factors. Existing approaches that pair text with financial time-series data based on simple keyword matching often fail to capture such complex relationships. To address this limitation, we propose a semantic-based and multi-level pairing framework. Specifically, we extract company-specific context for the target company from SEC filings and apply an embedding-based matching mechanism to retrieve semantically relevant news articles based on this context. Furthermore, we classify news articles into four levels (macro-level, sector-level, related company-level, and target company-level) using large language models (LLMs), enabling multi-level pairing of news articles with the target company. Applying this framework to publicly-available news datasets, we construct FinTexTS, a new large-scale text-paired stock price dataset. Experimental results on FinTexTS demonstrate the effectiveness of our semantic-based and multi-level pairing strategy in stock price forecasting. In addition to publicly-available news underlying FinTexTS, we show that applying our method to proprietary yet carefully curated news sources leads to higher-quality paired data and improved stock price forecasting performance.

Neural networks applied to financial time series operate in a regime of underspecification, where predictors achieve comparable out-of-sample error. Using large-scale volatility forecasting for S&P 500 stocks--twelve architecture-optimizer configurations, thirteen seeds each, evaluated on 564,795 held-out observations--we show that comparable test loss conceals measurably different predictors. In eleven of twelve comparisons, models trained from identical initialization and identical data order diverge $1.3$ to $7.8$ times further than repeated runs of either optimizer alone, ruling out initialization noise as the explanation. On a common scale, predictions differ by 5--17% of the typical forecast error while the models' error magnitudes differ by less than 0.7% of it. The divergence reshapes nonlinear response profiles, temporal dependence, and ultimately decisions: volatility-ranked portfolios trace a Sharpe-turnover frontier with up to 58% turnover dispersion at comparable gross Sharpe ratios. In underspecified settings, optimization is a consequential source of inductive bias, and model evaluation must extend beyond scalar loss to functional and decision-level behavior.

Forecasting financial asset returns is challenging due to low signal-to-noise ratios, non-stationarity and heavy-tailed distributions. We benchmark 16 deep learning architectures for time series forecasting, including Transformers, State Space Models (SSMs), xLSTMs and recurrent hybrids, on a 15-year daily futures dataset using an end-to-end volatility-targeted Sharpe ratio optimisation task. Our results challenge prevailing assumptions in the literature. Several widely used 'state-of-the-art' architectures, including generic Transformers and SSMs, underperformed a simple AR(1) benchmark in a realistic financial forecasting task. The strongest results came from comparatively simple hybrid approaches using recurrent structures: a Variable Selection Network combined with an LSTM achieved the highest Sharpe ratio, while xLSTM showed the greatest robustness to transaction costs. These findings suggest that success on standard time-series benchmarks does not reliably transfer to finance, and that architectures tailored to the unique properties of asset returns may remain more effective than generic attention-based approaches for financial forecasting.

Federated learning (FL) on graphs shows promise for distributed time-series forecasting. Yet, existing methods rely on static topologies and struggle with client heterogeneity. We propose Fed-GAME, a framework that models personalized aggregation as message passing over a learnable dynamic implicit graph. The core is a decoupled parameter difference-based update protocol, where clients transmit parameter differences between their fine-tuned private model and a shared global model. On the server, these differences are decomposed into two streams: (1) averaged difference used to updating the global model for consensus (2) the selective difference fed into a novel Graph Attention Mixture-of-Experts (GAME) aggregator for fine-grained personalization. In this aggregator, shared experts provide scoring signals while personalized gates adaptively weight selective updates to support personalized aggregation. Experiments on two real-world electric vehicle charging datasets demonstrate that Fed-GAME outperforms state-of-the-art personalized FL baselines.