Time Series Forecasting

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Overview

Time series forecasting studies how to predict future observations from past values, often across multiple horizons and with missing data, changing regimes, or external drivers such as weather and events. Methods range from classical autoregressive and exponential-smoothing models to recurrent networks, Transformers, state-space models, decomposition and frequency-based approaches, graph models, and pretrained foundation models; probabilistic methods also estimate uncertainty. Current work increasingly combines historical patterns with covariates, retrieval, domain knowledge, and online adaptation, while targeting applications from energy and weather to health, transport, and finance. A central tension is that larger or more complex models do not reliably beat simple baselines, and benchmark accuracy may not reflect robustness, forecast structure, uncertainty calibration, or downstream decision value.

Latest papers

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886 papers113 papers in the last four weeks, down 19% on the four weeks before. 0.7% of all new papers.

Mar 25, 2026

Forecasting with Guidance: Representation-Level Supervision for Time Series Forecasting

Nowadays, time series forecasting is predominantly approached through the end-to-end training of deep learning architectures using error-based objectives. While this is effective at minimizing average loss, it encourages the encoder to discard informative yet extreme patterns. This results in smooth predictions and temporal representations that poorly capture salient dynamics. To address this issue, we propose ReGuider, a plug-in method that can be seamlessly integrated into any forecasting architecture. ReGuider leverages pretrained time series foundation models as semantic teachers. During training, the input sequence is processed together by the target forecasting model and the pretrained model. Rather than using the pretrained model's outputs directly, we extract its intermediate embeddings, which are rich in temporal and semantic information, and align them with the target model's encoder embeddings through representation-level supervision. This alignment process enables the encoder to learn more expressive temporal representations, thereby improving the accuracy of downstream forecasting. Extensive experimentation across diverse datasets and architectures demonstrates that our ReGuider consistently improves forecasting performance, confirming its effectiveness and versatility.

Jiacheng Wang, Liang Fan, Baihua Li +1

Xijing University · Loughborough University · Northeastern University

Time Series ForecastingTime Series Representation LearningFeature-Based Knowledge Distillation
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Mar 25, 2026

IPatch: A Multi-Resolution Transformer Architecture for Robust Time-Series Forecasting

Accurate forecasting of multivariate time series remains challenging due to the need to capture both short-term fluctuations and long-range temporal dependencies. Transformer-based models have emerged as a powerful approach, but their performance depends critically on the representation of temporal data. Traditional point-wise representations preserve individual time-step information, enabling fine-grained modeling, yet they tend to be computationally expensive and less effective at modeling broader contextual dependencies, limiting their scalability to long sequences. Patch-wise representations aggregate consecutive steps into compact tokens to improve efficiency and model local temporal dynamics, but they often discard fine-grained temporal details that are critical for accurate predictions in volatile or complex time series. We propose IPatch, a multi-resolution Transformer architecture that integrates both point-wise and patch-wise tokens, modeling temporal information at multiple resolutions. Experiments on 7 benchmark datasets demonstrate that IPatch consistently improves forecasting accuracy, robustness to noise, and generalization across various prediction horizons compared to single-representation baselines.

Aymane Harkati, Moncef Garouani, Olivier Teste +2

CCPS Laboratory, ENSAM, Hassan II University, Casablanca, 20670, Morocco · IRIT, UMR 5505 CNRS, Université Toulouse Capitole, Toulouse, 31000, France · IRIT, UMR 5505 CNRS, Université Toulouse, UT2J, Toulouse, 31000, France

Robust Time Series ForecastingTime Series ForecastingMultivariate Time Series ForecastingTime Series TransformersMultiscale Time-Series Modeling
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Mar 24, 2026

A Comparative Study of Machine Learning Models for Hourly Forecasting of Air Temperature and Relative Humidity

Accurate short-term forecasting of air temperature and relative humidity is critical for urban management, especially in topographically complex cities such as Chongqing, China. This study compares seven machine learning models: eXtreme Gradient Boosting (XGBoost), Random Forest, Support Vector Regression (SVR), Multi-Layer Perceptron (MLP), Decision Tree, Long Short-Term Memory (LSTM) networks, and Convolutional Neural Network (CNN)-LSTM (CNN-LSTM), for hourly prediction using real-world open data. Based on a unified framework of data preprocessing, lag-feature construction, rolling statistical features, and time-series validation, the models are systematically evaluated in terms of predictive accuracy and robustness. The results show that XGBoost achieves the best overall performance, with a test mean absolute error (MAE) of 0.302 °C for air temperature and 1.271% for relative humidity, together with an average R2 of 0.989 across the two forecasting tasks. These findings demonstrate the strong effectiveness of tree-based ensemble learning for structured meteorological time-series forecasting and provide practical guidance for intelligent meteorological forecasting in mountainous cities.

Jiaqi Dong

Weather ForecastingTime Series ForecastingGradient-Boosted Decision Trees
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Mar 23, 2026

Cluster-Specific Predictive Modeling: A Scalable Solution for Resource-Constrained Wi-Fi Controllers

This manuscript presents a comprehensive analysis of predictive modeling optimization in managed Wi-Fi networks through the integration of clustering algorithms and model evaluation techniques. The study addresses the challenges of deploying forecasting algorithms in large-scale environments managed by a central controller constrained by memory and computational resources. Feature-based clustering, supported by Principal Component Analysis (PCA) and advanced feature engineering, is employed to group time series data based on shared characteristics, enabling the development of cluster-specific predictive models. Comparative evaluations between global models (GMs) and cluster-specific models demonstrate that cluster-specific models consistently achieve superior accuracy in terms of Mean Absolute Error (MAE) values in high-activity clusters. The trade-offs between model complexity (and accuracy) and resource utilization are analyzed, highlighting the scalability of tailored modeling approaches. The findings advocate for adaptive network management strategies that optimize resource allocation through selective model deployment, enhance predictive accuracy, and ensure scalable operations in large-scale, centrally managed Wi-Fi environments.

Gianluca Fontanesi, Luca Barbieri, Lorenzo Galati Giordano +2

Radio Systems Research, Nokia Bell Labs, Stuttgart, Germany · Nokia Spain, Madrid

Time Series ForecastingModel SelectionWireless Communications
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Mar 23, 2026

FISformer: Replacing Self-Attention with a Fuzzy Inference System in Transformer Models for Time Series Forecasting

Transformers have achieved remarkable progress in time series forecasting, yet their reliance on deterministic dot-product attention limits their capacity to model uncertainty and nonlinear dependencies across multivariate temporal dimensions. To address this limitation, we propose FISFormer, a Fuzzy Inference System-driven Transformer that replaces conventional attention with a FIS Interaction mechanism. In this framework, each query-key pair undergoes a fuzzy inference process for every feature dimension, where learnable membership functions and rule-based reasoning estimate token-wise relational strengths. These FIS-derived interaction weights capture uncertainty and provide interpretable, continuous mappings between tokens. A softmax operation is applied along the token axis to normalize these weights, which are then combined with the corresponding value features through element-wise multiplication to yield the final context-enhanced token representations. This design fuses the interpretability and uncertainty modeling of fuzzy logic with the representational power of Transformers. Extensive experiments on multiple benchmark datasets demonstrate that FISFormer achieves superior forecasting accuracy, noise robustness, and interpretability compared to state-of-the-art Transformer variants, establishing fuzzy inference as an effective alternative to conventional attention mechanisms.

Bulent Haznedar, Levent Karacan

Computer Engineering Department, Gaziantep University, Gaziantep, Türkiye

Time Series TransformersTime Series ForecastingTransformer AttentionMultivariate Time Series ForecastingFuzzy Logic
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Mar 23, 2026

Rethinking Multimodal Fusion for Time Series: Text Modalities Need Constrained Fusion

Recent advances in multimodal learning have motivated the integration of auxiliary modalities such as text or vision into time series (TS) forecasting. However, most existing methods provide limited gains, often improving performance only in specific datasets or relying on architecture-specific designs that limit generalization. In this paper, we show that multimodal models with naive fusion strategies (e.g., simple addition or concatenation) often underperform unimodal TS models, which we attribute to the uncontrolled integration of auxiliary modalities which may introduce irrelevant information. Motivated by this observation, we explore various constrained fusion methods designed to control such integration and find that they consistently outperform naive fusion methods. Furthermore, we propose Controlled Fusion Adapter (CFA), a simple plug-in method that enables controlled cross-modal interactions without modifying the TS backbone, integrating only relevant textual information aligned with TS dynamics. CFA employs low rank adapters to filter irrelevant textual information before fusing it into temporal representations. We conduct over 20K experiments across various datasets and TS/text models, demonstrating the effectiveness of the constrained fusion methods. Code is available at: https://github.com/seunghan96/cfa.

Seunghan Lee, Jun Seo, Jaehoon Lee +7

LG AI Research Seoul, South Korea

Cross-Modal LearningTime Series ForecastingMultimodal FusionData Fusion
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Mar 22, 2026

Benchmarking Scientific Machine Learning Models for Air Quality Data

Accurate air quality index (AQI) forecasting is essential for the protecting public health in rapidly growing urban regions, and the practical model evaluation and selection are often challenged by the lack of rigorous, region-specific benchmarking on standardized datasets. Physics-guided machine learning and deep learning models could be a good and effective solution to resolve such issues with more accurate and efficient AQI forecasting. This research study presents an explainable and comprehensive benchmark that enables a guideline and proposed physics-guided best model by benchmarking classical time-series, machine-learning, and deep-learning approaches for multi-horizon AQI forecasting in North Texas (Dallas County). Using publicly available U.S. Environmental Protection Agency (EPA) daily observations of air quality data from 2022 to 2024, we curate city-level time series for PM2.5 and O3 by aggregating station measurements and constructing lag-wise forecasting datasets for LAG in {1,7,14,30} days. For benchmarking the best model, linear regression (LR), SARIMAX, multilayer perceptrons (MLP), and LSTM networks are evaluated with the proposed physics-guided variants (MLP+Physics and LSTM+Physics) that incorporate the EPA breakpoint-based AQI formulation as a consistency constraint through a weighted loss. Experiments using chronological train-test splits and error metrics MAE, RMSE showed that deep-learning models outperform simpler baselines, while physics guidance improves stability and yields physically consistent pollutant with AQI relationships, with the largest benefits observed for short-horizon prediction and for PM2.5 and O3. Overall, the results provide a practical reference for selecting AQI forecasting models in North Texas and clarify when lightweight physics constraints meaningfully improve predictive performance across pollutants and forecast horizons.

Khawja Imran Masud, Venkata Sai Rahul Unnam, Sahara Ali

University of North Texas, 76205 Texas, USA

Air Quality PredictionForecasting BenchmarksTime Series ForecastingPhysics-Informed ML
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Mar 22, 2026

Long-Term Outlier Prediction Through Outlier Score Modeling

This study addresses an important gap in time series outlier detection by proposing a novel problem setting: long-term outlier prediction. Conventional methods primarily focus on immediate detection by identifying deviations from normal patterns. As a result, their applicability is limited when forecasting outlier events far into the future. To overcome this limitation, we propose a simple and unsupervised two-layer method that is independent of specific models. The first layer performs standard outlier detection, and the second layer predicts future outlier scores based on the temporal structure of previously observed outliers. This framework enables not only pointwise detection but also long-term forecasting of outlier likelihoods. Experiments on synthetic datasets show that the proposed method performs well in both detection and prediction tasks. These findings suggest that the method can serve as a strong baseline for future work in outlier detection and forecasting.

Yuma Aoki, Joon Park, Koh Takeuchi +6

Nara Institute of Science and Technology · Kyoto University · Panasonic Holdings Corporation

Time-Series Anomaly DetectionUnsupervised Anomaly DetectionTime Series Forecasting
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Mar 21, 2026

ReLaMix: Residual Latency-Aware Mixing for Delay-Robust Financial Time-Series Forecasting

Financial time-series forecasting in real-world high-frequency markets is often hindered by delayed or partially stale observations caused by asynchronous data acquisition and transmission latency. To better reflect such practical conditions, we investigate a simulated delay setting where a portion of historical signals is corrupted by a Zero-Order Hold (ZOH) mechanism, significantly increasing forecasting difficulty through stepwise stagnation artifacts. In this paper, we propose ReLaMix (Residual Latency-Aware Mixing Network), a lightweight extension of TimeMixer that integrates learnable bottleneck compression with residual refinement for robust signal recovery under delayed observations. ReLaMix explicitly suppresses redundancy from repeated stale values while preserving informative market dynamics via residual mixing enhancement. Experiments on a large-scale second-resolution PAXGUSDT benchmark demonstrate that ReLaMix consistently achieves state-of-the-art accuracy across multiple delay ratios and prediction horizons, outperforming strong mixer and Transformer baselines with substantially fewer parameters. Moreover, additional evaluations on BTCUSDT confirm the cross-asset generalization ability of the proposed framework. These results highlight the effectiveness of residual bottleneck mixing for high-frequency financial forecasting under realistic latency-induced staleness.

Tianyou Lai, Wentao Yue, Jiayi Zhou +5

Lanzhou University, Lanzhou, China · Brandeis University, Waltham, USA · Shenzhen University, Shenzhen, China +2

Robust Time Series ForecastingTime Series Forecasting
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Mar 21, 2026

Centrality-Based Pruning for Efficient Echo State Networks

Echo State Networks (ESNs) are a reservoir computing framework widely used for nonlinear time-series prediction. However, despite their effectiveness, randomly initialized reservoirs often contain redundant nodes, leading to unnecessary computational overhead and reduced efficiency. In this work, we propose a graph centrality-based pruning approach that interprets the reservoir as a weighted directed graph and removes structurally less important nodes using centrality measures. Experiments on Mackey-Glass time-series prediction and electric load forecasting demonstrate that the proposed method can significantly reduce reservoir size while maintaining, and in some cases improving, prediction accuracy.

Sudip Laudari

Independent Researcher.

Reservoir ComputingNeural Network PruningTime Series ForecastingDynamic Neural Networks
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Mar 20, 2026

Trojan horse hunt in deep forecasting models: Insights from the European Space Agency competition

Forecasting plays a crucial role in modern safety-critical applications, such as space operations. However, the increasing use of deep forecasting models introduces a new security risk of trojan horse attacks, carried out by hiding a backdoor in the training data or directly in the model weights. Once implanted, the backdoor is activated by a specific trigger pattern at test time, causing the model to produce manipulated predictions. We focus on this issue in our Trojan Horse Hunt data science competition, where more than 200 teams faced the task of identifying triggers hidden in deep forecasting models for spacecraft telemetry. We describe the novel task formulation, benchmark set, evaluation protocol, and best solutions from the competition. We further summarize key insights and research directions for effective identification of triggers in time series forecasting models. All materials are publicly available on the official competition webpage https://www.kaggle.com/competitions/trojan-horse-hunt-in-space.

Krzysztof Kotowski, Ramez Shendy, Jakub Nalepa +10

KP Labs, Bojkowska 37J, Gliwice, 44-100, Poland · Silesian University of Technology, Akademicka 16, Gliwice, 44-100, Poland · Warsaw University of Technology, Centre of Credible AI, Pl. Politechniki 1, Warsaw, 00-661, Poland +3

Backdoor DetectionTime Series Forecasting
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Mar 20, 2026

Fine-tuning Timeseries Predictors Using Reinforcement Learning

This chapter presents three major reinforcement learning algorithms used for fine-tuning financial forecasters. We propose a clear implementation plan for backpropagating the loss of a reinforcement learning task to a model trained using supervised learning, and compare the performance before and after the fine-tuning. We find an increase in performance after fine-tuning, and transfer learning properties to the models, indicating the benefits of fine-tuning. We also highlight the tuning process and empirical results for future implementation by practitioners.

Hugo Cazaux, Ralph Rudd, Hlynur Stefánsson +2

Reykjavik University, Department of Engineering, Menntavegur 1, Reykjavik, 102, Iceland

RL Fine-TuningTime Series Forecasting
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Mar 20, 2026

Deep Time-Series Forecasting in 10 Years: A Survey

Autocorrelation is a common property of time-series, where each observation is dependent on its predecessors. In deep time-series forecasting, it raises two central challenges: (1) designing backbone architectures to model autocorrelation in history sequences, and (2) devising loss functions to model autocorrelation in label sequences. Recent studies have made strides in tackling these challenges, but a systematic survey examining both aspects remains lacking. To bridge this gap, this paper reviews deep time-series forecasting from an autocorrelation modeling perspective, offering two contributions beyond existing surveys. First, it introduces a taxonomy that jointly covers both backbone architectures and loss functions, whereas prior surveys provide limited coverage of the latter. Second, it analyzes the motivations and insights underlying the surveyed literature from a unified autocorrelation perspective, providing a holistic overview of the field's evolution. Additional resources and details are available at https://github.com/Master-PLC/Awesome-TSF-Papers.

Hao Wang, Licheng Pan, Qingsong Wen +12

School of Intelligence Science and Technology, Peking University, Beijing 100871, China · School of Cyber Science and Technology, Zhejiang University, Hangzhou, Zhejiang 310027, China · Squirrel AI Learning, Bellevue, WA 98004, USA +7

Time Series Forecasting
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Mar 19, 2026

Rolling-Origin Validation Reverses Model Rankings in Multi-Step PM10 Forecasting: XGBoost, SARIMA, and Persistence

(a) Many air quality forecasting studies report gains from machine learning, but evaluations often use static chronological splits and omit persistence baselines, so the operational added value under routine updating is unclear. (b) Using 2,350 daily PM10 observations from 2017 to 2024 at an urban background monitoring station in southern Europe, we compare XGBoost and SARIMA against persistence under a static split and a rolling-origin protocol with monthly updates. We report horizon-specific skill and the predictability horizon, defined as the maximum horizon with positive persistence-relative skill. Static evaluation suggests XGBoost performs well from one to seven days ahead, but rolling-origin evaluation reverses rankings: XGBoost is not consistently better than persistence at short and intermediate horizons, whereas SARIMA remains positively skilled across the full range. (c) For researchers, static splits can overstate operational usefulness and change rankings. For practitioners, rolling-origin, persistence-referenced skill profiles show which methods stay reliable at each lead time.

Federico Garcia Crespi, Eduardo Yubero Funes, Marina Alfosea Simon

Departamento de Ingeniería de Computadores, Universidad Miguel Hernández, Elche, Spain · Departamento de Física Aplicada, Universidad Miguel Hernández, Elche, Spain

Time Series ForecastingAir Quality PredictionForecasting BenchmarksGradient-Boosted Decision Trees
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Mar 19, 2026

Extending SSMs with the Exponentially Weighted Signature

We introduce the exponentially weighted signature (EWS), a continuous-time model that computes iterated integrals of a path, where each increment is weighted by the matrix exponential of a learnable generator over elapsed clock time. We prove that it solves a linear controlled differential equation, keeps the group-like structure and the universality of the signature, and satisfies a modified Chen identity, enabling a parallel scan. At depth one the EWS is a state-space model (SSM), and we map linear time-invariant SSMs, Mamba channels and Mamba-22 heads to it in closed form. The EWS extends SSMs through an arbitrary matrix generator, a clock that generalises the step size to causal functionals of the input, and higher truncation depths that are non-linear in the path within a single layer. Empirically, the EWS achieves the highest average accuracy and rank on six long time-series classification datasets, where depth generally helps. Learned clocks prove necessary for state tracking on formal language tasks, and at depth one, the EWS matches or exceeds competing SSMs on regression and forecasting with far fewer parameters.

Alexandre Bloch, Benjamin Walker, Joël Mouterde +3

Mathematical Institute, University of Oxford · SKF · Department of Mathematics, Imperial College London

Dynamical SystemsTime Series ClassificationTime Series ForecastingState Space Models
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Mar 19, 2026

Adaptive Regime-Aware Stock Price Prediction Using Autoencoder-Gated Dual Node Transformers with Reinforcement Learning Control

Stock markets exhibit regime-dependent behavior where prediction models optimized for stable conditions often fail during volatile periods. Existing approaches typically treat all market states uniformly or require manual regime labeling, which is expensive and quickly becomes stale as market dynamics evolve. This paper introduces an adaptive prediction framework that adaptively identifies deviations from normal market conditions and routes data through specialized prediction pathways. The architecture consists of three components: (1) an autoencoder trained on normal market conditions that identifies anomalous regimes through reconstruction error, (2) dual node transformer networks specialized for stable and event-driven market conditions respectively, and (3) a Soft Actor-Critic reinforcement learning controller that adaptively tunes the regime detection threshold and pathway blending weights based on prediction performance feedback. The reinforcement learning component enables the system to learn adaptive regime boundaries, defining anomalies as market states where standard prediction approaches fail. Experiments on 20 S&P 500 stocks spanning 1982 to 2025 demonstrate that the proposed framework achieves 0.68% mean absolute percentage error (MAPE) for one-day predictions without the reinforcement controller and 0.59% MAPE with the full adaptive system, compared to 0.80% for the baseline integrated node transformer. Directional accuracy reaches 72% with the complete framework. The system maintains robust performance during high-volatility periods, with MAPE below 0.85% when baseline models exceed 1.5%. Ablation studies confirm that each component contributes meaningfully: autoencoder routing accounts for 36% relative MAPE degradation upon removal, followed by the SAC controller at 15% and the dual-path architecture at 7%.

Mohammad Al Ridhawi, Mahtab Haj Ali, Hussein Al Osman

School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Canada

Time Series ForecastingFinanceTime Series TransformersRegime-Switching Dynamical Systems
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Mar 19, 2026

MLOW: Interpretable Low-Rank Frequency Magnitude Decomposition of Multiple Effects for Time Series Forecasting

Separating multiple effects in time series is fundamental yet challenging for time-series forecasting (TSF). However, existing TSF models cannot effectively learn interpretable multi-effect decomposition by their smoothing-based temporal techniques. Here, a new interpretable frequency-based decomposition pipeline MLOW captures the insight: a time series can be represented as a magnitude spectrum multiplied by the corresponding phase-aware basis functions, and the magnitude spectrum distribution of a time series always exhibits observable patterns for different effects. MLOW learns a low-rank representation of the magnitude spectrum to capture dominant trending and seasonal effects. We explore low-rank methods, including PCA, NMF, and Semi-NMF, and find that none can simultaneously achieve interpretable, efficient and generalizable decomposition. Thus, we propose hyperplane-nonnegative matrix factorization (Hyperplane-NMF). Further, to address the frequency (spectral) leakage restricting high-quality low-rank decomposition, MLOW enables a flexible selection of input horizons and frequency levels via a mathematical mechanism. Visual analysis demonstrates that MLOW enables interpretable and hierarchical multiple-effect decomposition, robust to noises. It can also enable plug-and-play in existing TSF backbones with remarkable performance improvement but minimal architectural modifications.

Runze Yang, Longbing Cao, Xiaoming Wu +4

1Macquarie University · 2Shanghai Jiao Tong University · 3Nanyang Technological University +1

Frequency-Domain Time Series ModelingTime Series ForecastingTime Series DecompositionExplainable Time Series ForecastingLow-Rank Matrix DecompositionFrequency-Domain Analysis
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Mar 18, 2026

Baguan-TS: A Sequence-Native In-Context Learning Model for Time Series Forecasting with Covariates

Transformers enable in-context learning (ICL) for rapid, gradient-free adaptation in time series forecasting, yet most ICL-style approaches rely on tabularized, hand-crafted features, while end-to-end sequence models lack inference-time adaptation. We bridge this gap with a unified framework, Baguan-TS, which integrates the raw-sequence representation learning with ICL, instantiated by a 3D Transformer that attends jointly over temporal, variable, and context axes. To make this high-capacity model practical, we tackle two key hurdles: (i) calibration and training stability, improved with a feature-agnostic, target-space retrieval-based local calibration; and (ii) output oversmoothing, mitigated via context-overfitting strategy. On public benchmark with covariates, Baguan-TS consistently outperforms established baselines, achieving the highest win rate and significant reductions in both point and probabilistic forecasting metrics. Further evaluations across diverse real-world energy datasets demonstrate its robustness, yielding substantial improvements.

Linxiao Yang, Xue Jiang, Gezheng Xu +9

DAMO Academy, Alibaba Group, Hangzhou, China

Time Series ForecastingMultivariate Time Series ForecastingTime Series Forecasting with CovariatesTime Series Transformers
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Mar 18, 2026

The Phasor Transformer: Resolving Attention Bottlenecks on the Unit Circle

Transformer models have redefined sequence learning, yet dot-product self-attention introduces a quadratic token-mixing bottleneck for long-context time-series. We introduce the Phasor Transformer block, a phase-native alternative representing sequence states on the unit-circle manifold S1S^1. Each block combines lightweight trainable phase-shifts with parameter-free Discrete Fourier Transform (DFT) token coupling, achieving global O(Nlog⁡N)\mathcal{O}(N\log N) mixing without explicit attention maps. Stacking these blocks defines the Large Phasor Model (LPM). We validate LPM on autoregressive time-series prediction over synthetic multi-frequency benchmarks against honest baselines: it beats a zero-parameter persistence baseline and, with the corrected gradient path, improves monotonically with depth before saturating, while remaining competitive-but-not-superior to self-attention at a fraction of the parameter count. Our results establish an explicit efficiency--accuracy frontier, showing that scalable temporal modeling in oscillatory domains can emerge from geometry-constrained phase computation with deterministic global coupling.

Dibakar Sigdel

Mindverse Computing LLC, WA 98087

TransformerTime Series ForecastingTime Series Transformers
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Mar 17, 2026

Beyond Accuracy: Evaluating Forecasting Models by Multi-Echelon Inventory Cost

This study develops a digitalized forecasting-inventory optimization pipeline integrating traditional forecasting models, machine learning regressors, and deep sequence models within a unified inventory simulation framework. Using the M5 Walmart dataset, we evaluate seven forecasting approaches and assess their operational impact under single- and two-echelon newsvendor systems. Results indicate that Temporal CNN and LSTM models significantly reduce inventory costs and improve fill rates compared to statistical baselines. Sensitivity and multi-echelon analyses demonstrate robustness and scalability, offering a data-driven decision-support tool for modern supply chains.

Swata Marik, Swayamjit Saha, Garga Chatterjee

Department of Home Science, University of Calcutta, 20 E, Judges Court Road, Alipore, Kolkata, 700027, West Bengal, India. · Department of Computer Science and Engineering, Mississippi State University, 665 George Perry Street, Starkville, 39759, MS, USA. · Psychology Research Unit, Indian Statistical Institute Kolkata, 203, B.T. Road, Kolkata, 700108, West Bengal, India.

Inventory ControlTime Series ForecastingForecasting Benchmarks
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Mar 17, 2026

Integrating Inductive Biases in Transformers via Distillation for Financial Time Series Forecasting

Transformer-based models have been widely adopted for time-series forecasting due to their high representational capacity and architectural flexibility. However, many Transformer variants implicitly assume stationarity and stable temporal dynamics -- assumptions routinely violated in financial markets characterized by regime shifts and non-stationarity. Empirically, state-of-the-art time-series Transformers often underperform even vanilla Transformers on financial tasks, while simpler architectures with distinct inductive biases, such as CNNs and RNNs, can achieve stronger performance with substantially lower complexity. At the same time, no single inductive bias dominates across markets or regimes, suggesting that robust financial forecasting requires integrating complementary temporal priors. We propose TIPS (Transformer with Inductive Prior Synthesis), a knowledge distillation framework that synthesizes diverse inductive biases -- causality, locality, and periodicity -- within a unified Transformer. TIPS trains bias-specialized Transformer teachers via attention masking, then distills their knowledge into a single student model with regime-dependent alignment across inductive biases. Across four major equity markets, TIPS achieves state-of-the-art performance, outperforming strong ensemble baselines by 55%, 9%, and 16% in annual return, Sharpe ratio, and Calmar ratio, while requiring only 38% of the inference-time computation. Further analyses show that TIPS generates statistically significant excess returns beyond both vanilla Transformers and its teacher ensembles, and exhibits regime-dependent behavioral alignment with classical architectures during their profitable periods. These results highlight the importance of regime-dependent inductive bias utilization for robust generalization in non-stationary financial time series.

Yu-Chen Den, Kuan-Yu Chen, Kendro Vincent +1

SinoPac Holdings, Taipei, Taiwan · National Chengchi University, Taipei, Taiwan

Time Series ForecastingFinancial Time SeriesTime Series TransformersNon-Stationary Time Series ForecastingKnowledge Distillation
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Mar 17, 2026

msData: A Millisecond-Resolution Network Dataset for Advancing Time Series Foundation Models

Time series foundation models (TSFMs) require diverse, real-world datasets to adapt across varying domains and temporal frequencies. However, current large-scale datasets predominantly focus on low-frequency time series with sampling intervals, i.e., time resolution, in the range of seconds to years, hindering their ability to capture the nuances of high-frequency time series data. To address this limitation, we introduce a novel dataset, msData, that captures millisecond-resolution wireless and traffic conditions from an operational 5G wireless deployment, expanding the scope of TSFMs to incorporate high-frequency data for pre-training. Further, the dataset introduces a new domain, namely, wireless networks, thus complementing existing more general domains like energy and finance. The dataset also provides use cases for short-term forecasting, with prediction horizons spanning from 1 millisecond (1 step) to 96 milliseconds (96 steps). To demonstrate the utility of the dataset, we benchmark traditional machine learning models, transformer-based deep learning models, and TSFMs on forecasting tasks using representative subsets of the data, including a static mobility pattern within YouTube traffic class and a train mobility pattern within Web Browsing traffic class. Across these data distributions, we demonstrate that most TSFM model configurations perform poorly in both zero-shot and fine-tuned settings. Our work underscores the importance of incorporating high-frequency datasets during pre-training and forecasting to enhance architectures, fine-tuning strategies, generalization, and robustness of TSFMs in real-world applications. Code is available at this repository: https://github.com/khanalsubina/msData. Data is available on: Hugging Face.

Subina Khanal, Seshu Tirupathi, Merim Dzaferagic +2

Department of Computer Science Aalborg University · IBM Research, Ireland · Trinity College Dublin

Wireless Local Area NetworksTime-Series Foundation ModelsTime Series ForecastingForecasting BenchmarksWireless Communications
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Mar 16, 2026

Time-Aware Prior Fitted Networks for Zero-Shot Forecasting with Exogenous Variables

In many time series forecasting settings, the target time series is accompanied by exogenous covariates, such as promotions and prices in retail demand; temperature in energy load; calendar and holiday indicators for traffic or sales; and grid load or fuel costs in electricity pricing. Ignoring these exogenous signals can substantially degrade forecasting accuracy, particularly when they drive spikes, discontinuities, or regime and phase changes in the target series. Most current time series foundation models (e.g., Chronos, Sundial, TimesFM, TimeMoE, TimeLLM, and LagLlama) ignore exogenous covariates and make forecasts solely from the numerical time series history, thereby limiting their performance. In this paper, we develop ApolloPFN, a prior-data fitted network (PFN) that is time-aware (unlike prior PFNs) and that natively incorporates exogenous covariates (unlike prior univariate forecasters). Our design introduces two major advances: (i) a synthetic data generation framework that injects realistic temporal patterns, structural changes, and exogenous dependencies into the PFN prior; and (ii) time-aware architectural modifications that embed inductive biases needed to exploit temporal context. We demonstrate that ApolloPFN outperforms existing baselines across several forecasting benchmarks with exogenous information, including M5, electric price forecasting, UCI Air Quality, and Solar Energy datasets.

Andres Potapczynski, Ravi Kiran Selvam, Tatiana Konstantinova +7

Amazon Science, New York University · Amazon Science

Exogenous Time Series ForecastingTime Series ForecastingTime Series Forecasting with CovariatesZero-Shot Time Series ForecastingPrior-Data Fitted NetworksTime-Series Foundation Models
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Mar 16, 2026

Seeking SOTA: Time-Series Forecasting Must Adopt Taxonomy-Specific Evaluation to Dispel Illusory Gains

We argue that the current practice of evaluating AI/ML time-series forecasting models, predominantly on benchmarks characterized by strong, persistent periodicities and seasonalities, obscures real progress by overlooking the performance of efficient classical methods. We demonstrate that these "standard" datasets often exhibit dominant autocorrelation patterns and seasonal cycles that can be effectively captured by simpler linear or statistical models, rendering complex deep learning architectures frequently no more performant than their classical counterparts for these specific data characteristics, and raising questions as to whether any marginal improvements justify the significant increase in computational overhead and model complexity. We call on the community to (I) retire or substantially augment current benchmarks with datasets exhibiting a wider spectrum of non-stationarities, such as structural breaks, time-varying volatility, and concept drift, and less predictable dynamics drawn from diverse real-world domains, and (II) require every deep learning submission to include robust classical and simple baselines, appropriately chosen for the specific characteristics of the downstream tasks' time series. By doing so, we will help ensure that reported gains reflect genuine scientific methodological advances rather than artifacts of benchmark selection favoring models adept at learning repetitive patterns.

Raeid Saqur, Christoph Bergmeir, Blanka Horvath +3

Dept. of Computer Science, University of Toronto · Dept. of Mathematics, University of Oxford · Vector Institute +5

Time Series ForecastingTime Series ModelingForecasting BenchmarksNon-Stationary Time Series
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Mar 16, 2026

Unlocking the Value of Text: Event-Driven Reasoning and Multi-Level Alignment for Time Series Forecasting

Existing time series forecasting methods primarily rely on the numerical data itself. However, real-world time series exhibit complex patterns associated with multimodal information, making them difficult to predict with numerical data alone. While several multimodal time series forecasting methods have emerged, they either utilize text with limited supplementary information or focus merely on representation extraction, extracting minimal textual information for forecasting. To unlock the Value of Text, we propose VoT, a method with Event-driven Reasoning and Multi-level Alignment. Event-driven Reasoning combines the rich information in exogenous text with the powerful reasoning capabilities of LLMs for time series forecasting. To guide the LLMs in effective reasoning, we propose the Historical In-context Learning that retrieves and applies historical examples as in-context guidance. To maximize the utilization of text, we propose Multi-level Alignment. At the representation level, we utilize the Endogenous Text Alignment to integrate the endogenous text information with the time series. At the prediction level, we design the Adaptive Frequency Fusion to fuse the frequency components of event-driven prediction and numerical prediction to achieve complementary advantages. Experiments on real-world datasets across 10 domains demonstrate significant improvements over existing methods, validating the effectiveness of our approach in the utilization of text. The code is made available at https://github.com/decisionintelligence/VoT.

Siyuan Wang, Peng Chen, Yihang Wang +4

East China Normal University

Time Series ForecastingLLM-Based Time Series ForecastingTime Series ReasoningMultivariate Time Series ForecastingRetrieval-Augmented Time Series Forecasting
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Mar 16, 2026

Integrating Weather Foundation Model and Satellite to Enable Fine-Grained Solar Irradiance Forecasting

Accurate day-ahead solar irradiance forecasting is essential for integrating solar energy into the power grid. However, it remains challenging due to the pronounced diurnal cycle and inherently complex cloud dynamics. Current methods either lack fine-scale resolution (e.g., numerical weather prediction, weather foundation models) or degrade at longer lead times (e.g., satellite extrapolation). We propose Baguan-solar, a two-stage multimodal framework that fuses forecasts from Baguan, a global weather foundation model, with high-resolution geostationary satellite imagery to produce 24-hour irradiance forecasts at kilometer scale. Its decoupled two-stage design first forecasts day-night continuous intermediates (e.g., cloud cover) and then infers irradiance, while its modality fusion jointly preserves fine-scale cloud structures from satellite and large-scale constraints from Baguan forecasts. Evaluated over East Asia using CLDAS as ground truth, Baguan-solar outperforms strong baselines (including ECMWF IFS, vanilla Baguan, and SolarSeer), reducing RMSE by 16.08% and better resolving cloud-induced transients. An operational deployment of Baguan-solar has supported solar power forecasting in an eastern province in China, since July 2025. Our code is accessible at https://github.com/DAMO-DI-ML/Baguan-solar.git.

Ziqing Ma, Kai Ying, Xinyue Gu +7

DAMO Academy, Alibaba Group, Hangzhou, Zhejiang, China · College of Computer Science, Zhejiang University of Technology, Hangzhou, Zhejiang, China · DAMO Academy, Alibaba Group, Bellevue, USA

Solar Irradiance ForecastingSolar Power ForecastingSpatiotemporal ForecastingTime Series ForecastingWeather ForecastingMultimodal Fusion
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Mar 16, 2026

GARCH-FIS: A Hybrid Forecasting Model with Dynamic Volatility-Driven Parameter Adaptation

This paper proposes a novel hybrid model, termed GARCH-FIS, for recursive rolling multi-step forecasting of financial time series. It integrates a Fuzzy Inference System (FIS) with a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to jointly address nonlinear dynamics and time-varying volatility. The core innovation is a dynamic parameter adaptation mechanism for the FIS, specifically activated within the multi-step forecasting cycle. In this process, the conditional volatility estimated by a rolling window GARCH model is continuously translated into a price volatility measure. At each forecasting step, this measure, alongside the updated mean of the sliding window data -- which now incorporates the most recent predicted price -- jointly determines the parameters of the FIS membership functions for the next prediction. Consequently, the granularity of the fuzzy inference adapts as the forecast horizon extends: membership functions are automatically widened during high-volatility market regimes to bolster robustness and narrowed during stable periods to enhance precision. This constitutes a fundamental advancement over a static one-step-ahead prediction setup. Furthermore, the model's fuzzy rule base is automatically constructed from data using the Wang-Mendel method, promoting interpretability and adaptability. Empirical evaluation, focused exclusively on multi-step forecasting performance across ten diverse financial assets, demonstrates that the proposed GARCH-FIS model significantly outperforms benchmark models -- including Support Vector Regression(SVR), Long Short-Term Memory networks(LSTM), and an ARIMA-GARCH econometric model -- in terms of predictive accuracy and stability, while effectively mitigating error accumulation in extended recursive forecasts.

Wen-Jing Li, Da-Qing Zhang

School of Science, University of Science and Technology Liaoning, Anshan, Liaoning Province, 114051, PR China

Time Series ForecastingFinancial Time SeriesFuzzy Logic
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Mar 16, 2026

Not All Retrievals are Useful: Cross-Attention for Input-Aware RAG in Time Series Forecasting

Retrieval-augmented generation (RAG) enhances zero-shot time series (TS) forecasting by leveraging external knowledge bases, yet existing approaches overlook input-level relevance when fusing retrieved samples with the query. We argue that not all retrievals are equally useful, and irrelevant ones can degrade performance. To this end, we propose Cross-RAG, a zero-shot RAG-based forecasting framework that selectively attends to query-relevant retrieved samples via query--retrieval cross-attention. By modeling input-level relevance between the query and retrieved samples, Cross-RAG jointly incorporates three sources of information: 1) the query itself, 2) the retrieved samples, and 3) their relational interactions. In particular, this input-aware design enables Cross-RAG to remain stable as the number of retrieved samples kk grows, whereas prior methods without cross-attention require careful kk tuning to avoid degradation from irrelevant retrievals. Extensive experiments demonstrate that Cross-RAG consistently improves zero-shot forecasting performance across multiple TSFM backbones and various RAG methods, with additional analyses confirming its effectiveness across various retrieval scenarios. Code is available at https://github.com/seunghan96/cross-rag/.

Seunghan Lee, Jaehoon Lee, Jun Seo +7

LG AI Research Seoul, South Korea

Zero-Shot Time Series ForecastingCross-AttentionTime Series ForecastingAttention MechanismsRetrieval-Augmented Time Series Forecasting
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Mar 14, 2026

Gated Graph Attention Networks for Predicting Duration of Large Scale Power Outages Induced by Natural Disasters

The occurrence of large-scale power outages induced by natural disasters has been on the rise in a changing climate. Such power outages often last extended durations, causing substantial financial losses and socioeconomic impacts to customers. Accurate estimation of outage duration is thus critical for enhancing the resilience of energy infrastructure under severe weather. We formulate such a task as a machine learning (ML) problem with focus on unique real-world challenges: high-order spatial dependency in the data, a moderate number of large-scale outage events, heterogeneous types of such events, and different impacts in a region within each event. To address these challenges, we develop a Bimodal Gated Graph Attention Network (BiGGAT), a graph-based neural network model, that integrates a Graph Attention Network (GAT) with a Gated Recurrent Unit (GRU) to capture the complex spatial characteristics. We evaluate the approach in a setting of inductive learning, using large-scale power outage data from six major hurricanes in the Southeastern United States. Experimental results demonstrate that BiGGAT achieves a superior performance compared to benchmark models.

Chenghao Duan, Chuanyi Ji, Anwar Walid +1

School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA · Department of Electrical Engineering, Columbia University, New York, NY, USA · School of Business, University of California, Riverside, Riverside, CA, USA

Power SystemsGraph Attention NetworksTime Series Forecasting
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Mar 13, 2026

Competition-Aware CPC Forecasting with Near-Market Coverage

Cost-per-click (CPC) in paid search is an auction-generated outcome shaped by a competitive landscape that is only partially observable from any single advertiser's history. From 1.66 billion Google Ads log records for a concentrated car-rental market (2021-2023), we construct a weekly panel of 1,811 keyword series over 127 weeks (218,924 keyword-week observations) and build competition-aware proxies from keyword text, CPC trajectories, and geographic market structure. The design combines (i) semantic neighborhoods and a semantic keyword graph from pretrained transformer-based keyword representations, (ii) behavioral neighborhoods from Dynamic Time Warping (DTW) alignment of CPC trajectories, and (iii) geographic-intent covariates capturing localized demand and marketplace heterogeneity. We evaluate these signals both as exogenous covariates and as relational priors in spatiotemporal graph forecasters, benchmarking them against statistical, neural, and time-series foundation-model baselines. The results reveal a clear horizon crossover. At one week, graph-based models achieve the lowest error, reducing sMAPE by 15.1% relative to the strongest classical/ML baseline; at the six- and twelve-week horizons, covariate-augmented foundation models dominate, reducing sMAPE by 22.5% and 27.6%, respectively. The gains concentrate in the high-CPC, high-volatility keywords where forecasting errors are most costly. A falsification battery supports the competition interpretation at the planning horizon: the semantic competition graph outperforms a confounder-matched non-competitive graph by 4.05 sMAPE points, and matched-neighbour and time-shuffled controls show the six-week gains are competition-specific rather than generic smoothing. Together, the findings establish a horizon-dependent competition-aware forecasting design for auction-driven advertising markets under partial observability.

Sebastian Frey, Edoardo Beccari, Maximilian Kranz +4

*Nova School of Business and Economics, Portugal · †University of Hamburg, Germany

Competitive AnalysisOnline AdvertisingTime Series ForecastingTime-Series Foundation ModelsSpatiotemporal GNNs
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