Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many existing approaches do not explicitly model the dynamics. To bridge this gap, we introduce DeepEDM, a framework that integrates nonlinear dynamical systems modeling with deep neural networks. Inspired by empirical dynamic modeling (EDM) and rooted in Takens' theorem, DeepEDM presents a novel deep model that learns a latent space from time-delayed embeddings, and employs kernel regression to approximate the underlying dynamics, while leveraging efficient implementation of softmax attention and allowing for accurate prediction of future time steps. To evaluate our method, we conduct comprehensive experiments on synthetic data of nonlinear dynamical systems as well as real-world time series across domains. Our results show that DeepEDM is robust to input noise, and outperforms state-of-the-art methods in forecasting accuracy. Our code is available at: https://abrarmajeedi.github.io/deep_edm.
With the advent of Transformers, time series forecasting has seen significant advances, yet it remains challenging due to the need for effective sequence representation, memory construction, and accurate target projection. Time series forecasting remains a challenging task, demanding effective sequence representation, meaningful information extraction, and precise future projection. Each dataset and forecasting configuration constitutes a distinct task, each posing unique challenges the model must overcome to produce accurate predictions. To systematically address these task-specific difficulties, this work decomposes the time series forecasting pipeline into three core stages: input sequence representation, information extraction and memory construction, and final target projection. Within each stage, we investigate a range of architectural configurations to assess the effectiveness of various modules, such as convolutional layers for feature extraction and self-attention mechanisms for information extraction, across diverse forecasting tasks, including evaluations on seven benchmark datasets. Our models achieve state-of-the-art forecasting accuracy while greatly enhancing computational efficiency, with reduced training and inference times and a lower parameter count. The source code is available at https://github.com/RobertLeppich/REP-Net.
Large Language Models (LLMs) have shown remarkable performance across diverse tasks without domain-specific training, fueling interest in their potential for time-series forecasting. While LLMs have shown potential in zero-shot forecasting through prompting alone, recent studies suggest that LLMs lack inherent effectiveness in forecasting. Given these conflicting findings, a rigorous validation is essential for drawing reliable conclusions. In this paper, we evaluate the effectiveness of LLMs as zero-shot forecasters compared to state-of-the-art domain-specific models. Our experiments show that LLM-based zero-shot forecasters often struggle to achieve high accuracy due to their sensitivity to noise, underperforming even simple domain-specific models. We have explored solutions to reduce LLMs' sensitivity to noise in the zero-shot setting, but improving their robustness remains a significant challenge. Our findings suggest that rather than emphasizing zero-shot forecasting, a more promising direction would be to focus on fine-tuning LLMs to better process numerical sequences. Our experimental code is available at https://github.com/junwoopark92/revisiting-LLMs-zeroshot-forecaster.
As a prominent data modality task, time series forecasting plays a pivotal role in diverse applications. With the remarkable advancements in Large Language Models (LLMs), the adoption of LLMs as the foundational architecture for time series modeling has gained significant attention. Although existing models achieve some success, they rarely both model time and frequency characteristics in a pretraining-finetuning paradigm leading to suboptimal performance in predictions of complex time series, which requires both modeling periodicity and prior pattern knowledge of signals. We propose MoFE-Time, an innovative time series forecasting model that integrates time and frequency domain features within a Mixture of Experts (MoE) network. Moreover, we use the pretraining-finetuning paradigm as our training framework to effectively transfer prior pattern knowledge across pretraining and finetuning datasets with different periodicity distributions. Our method introduces both frequency and time cells as experts after attention modules and leverages the MoE routing mechanism to construct multidimensional sparse representations of input signals. In experiments on six public benchmarks, MoFE-Time has achieved new state-of-the-art performance, reducing MSE and MAE by 6.95% and 6.02% compared to the representative methods Time-MoE. Beyond the existing evaluation benchmarks, we have developed a proprietary dataset, NEV-sales, derived from real-world business scenarios. Our method achieves outstanding results on this dataset, underscoring the effectiveness of the MoFE-Time model in practical commercial applications.
Deep learning-based approaches have demonstrated significant advancements in time series forecasting. Despite these ongoing developments, the complex dynamics of time series make it challenging to establish the rule of thumb for designing the golden model architecture. In this study, we argue that refining existing advanced models through a universal calibrating strategy can deliver substantial benefits with minimal resource costs, as opposed to elaborating and training a new model from scratch. We first identify a multi-target learning conflict in the calibrating process, which arises when optimizing variables across time steps, leading to the underutilization of the model's learning capabilities. To address this issue, we propose an innovative calibrating strategy called Socket+Plug (SoP). This approach retains an exclusive optimizer and early-stopping monitor for each predicted target within each Plug while keeping the fully trained Socket backbone frozen. The model-agnostic nature of SoP allows it to directly calibrate the performance of any trained deep forecasting models, regardless of their specific architectures. Extensive experiments on various time series benchmarks and a spatio-temporal meteorological ERA5 dataset demonstrate the effectiveness of SoP, achieving up to a 22% improvement even when employing a simple MLP as the Plug (highlighted in Figure 1)
Learning from multi-variate time-series with heterogeneous channel configurations remains a fundamental challenge for deep neural networks (DNNs), particularly in clinical domains such as intracranial electroencephalography (iEEG), where channel setups vary widely across subjects. In this work, we introduce multi-variate parallel attention (MVPA), a novel self-attention mechanism that disentangles content, temporal, and spatial attention, enabling flexible, generalizable, and efficient modeling of time-series data with varying channel counts and configurations. We use MVPA to build MVPFormer, a generative foundation model for human electrophysiology, trained to predict the evolution of iEEG signals across diverse subjects. To support this and future effort by the community, we release the SWEC iEEG dataset, the largest publicly available iEEG dataset to date, comprising nearly 10,000 hours of recordings from heterogeneous clinical sources. MVPFormer leverages MVPA to achieve strong generalization across subjects, demonstrating expert-level performance in seizure detection and outperforming state-of-the-art Transformer baselines on our SWEC, the MAYO, and the FNUSA dataset. We further validate MVPA on standard time-series forecasting and classification tasks, where it matches or exceeds existing attention-based models. Together, our contributions establish MVPA as a general-purpose attention mechanism for heterogeneous time-series and MVPFormer as the first open-source, open-weights, and open-data iEEG foundation model with state-of-the-art clinical performance. The code is available at https://github.com/IBM/multi-variate-parallel-transformer. The SWEC iEEG dataset is available at https://mb-neuro.medical-blocks.ch/public_access/databases/ieeg/swec_ieeg.
Accurate electrical consumption forecasting is crucial for efficient energy management and resource allocation. While traditional time series forecasting relies on historical patterns and temporal dependencies, incorporating external factors -- such as weather indicators -- has shown significant potential for improving prediction accuracy in complex real-world applications. However, the inclusion of these additional features often degrades the performance of global predictive models trained on entire populations, despite improving individual household-level models. To address this challenge, we found that a hypernetwork architecture can effectively leverage external factors to enhance the accuracy of global electrical consumption forecasting models, by specifically adjusting the model weights to each consumer. We collected a comprehensive dataset spanning two years, comprising consumption data from over 6000 luxembourgish households and corresponding external factors such as weather indicators, holidays, and major local events. By comparing various forecasting models, we demonstrate that a hypernetwork approach outperforms existing methods when associated to external factors, reducing forecasting errors and achieving the best accuracy while maintaining the benefits of a global model.
Accurate weather forecasts are essential for supporting a wide range of activities and decision-making processes, as well as mitigating the impacts of adverse weather events. While traditional numerical weather prediction (NWP) remains the cornerstone of operational forecasting, machine learning is emerging as a powerful alternative for fast, flexible, and scalable predictions. We introduce PeakWeather, a high-quality dataset of surface weather observations collected every 10 minutes over more than 8 years from the ground stations of the Federal Office of Meteorology and Climatology MeteoSwiss's measurement network. The dataset includes a diverse set of meteorological variables from 302 station locations distributed across Switzerland's complex topography and is complemented with topographical indices derived from digital height models for context. Ensemble forecasts from the currently operational high-resolution NWP model are provided as a baseline forecast against which to evaluate new approaches. The dataset's richness supports a broad spectrum of spatiotemporal tasks, including time series forecasting at various scales, graph structure learning, imputation, and virtual sensing. As such, PeakWeather serves as a real-world benchmark to advance both foundational machine learning research, meteorology, and sensor-based applications.
To advance time series forecasting (TSF), various methods have been proposed to improve prediction accuracy, evolving from statistical techniques to data-driven deep learning architectures. Despite their effectiveness, most existing methods still adhere to a fast thinking paradigm-relying on extracting historical patterns and mapping them to future values as their core modeling philosophy, lacking an explicit thinking process that incorporates intermediate time series reasoning. Meanwhile, emerging slow-thinking LLMs (e.g., OpenAI-o1) have shown remarkable multi-step reasoning capabilities, offering an alternative way to overcome these issues. However, prompt engineering alone presents several limitations - including high computational cost, privacy risks, and limited capacity for in-depth domain-specific time series reasoning. To address these limitations, a more promising approach is to train LLMs to develop slow thinking capabilities and acquire strong time series reasoning skills. For this purpose, we propose Time-R1, a two-stage reinforcement fine-tuning framework designed to enhance multi-step reasoning ability of LLMs for time series forecasting. Specifically, the first stage conducts supervised fine-tuning for warmup adaptation, while the second stage employs reinforcement learning to improve the model's generalization ability. Particularly, we design a fine-grained multi-objective reward specifically for time series forecasting, and then introduce GRIP (group-based relative importance for policy optimization), which leverages non-uniform sampling to further encourage and optimize the model's exploration of effective reasoning paths. Experiments demonstrate that Time-R1 significantly improves forecast performance across diverse datasets.
Multivariate long-term and efficient time series forecasting is a key requirement for a variety of practical applications, and there are complex interleaving time dynamics in time series data that require decomposition modeling. Traditional time series decomposition methods are single and rely on fixed rules, which are insufficient for mining the potential information of the series and adapting to the dynamic characteristics of complex series. On the other hand, the Transformer-based models for time series forecasting struggle to effectively model long sequences and intricate dynamic relationships due to their high computational complexity. To overcome these limitations, we introduce KARMA, with an Adaptive Time Channel Decomposition module (ATCD) to dynamically extract trend and seasonal components. It further integrates a Hybrid Frequency-Time Decomposition module (HFTD) to further decompose Series into frequency-domain and time-domain. These components are coupled with multi-scale Mamba-based KarmaBlock to efficiently process global and local information in a coordinated manner. Experiments on eight real-world datasets from diverse domains well demonstrated that KARMA significantly outperforms mainstream baseline methods in both predictive accuracy and computational efficiency. Code and full results are available at this repository: https://github.com/yedadasd/KARMA
Developments in Deep Learning have significantly improved time series forecasting by enabling more accurate modeling of complex temporal dependencies inherent in sequential data. The effectiveness of such models is often demonstrated on limited sets of specific real-world data. Although this allows for comparative analysis, it still does not demonstrate how specific data characteristics align with the architectural strengths of individual models. Our research aims at uncovering clear connections between time series characteristics and particular models. We introduce a novel dataset generated using Gaussian Processes, specifically designed to display distinct, known characteristics for targeted evaluations of model adaptability to them. Furthermore, we present TimeFlex, a new model that incorporates a modular architecture tailored to handle diverse temporal dynamics, including trends and periodic patterns. This model is compared to current state-of-the-art models, offering a deeper understanding of how models perform under varied time series conditions.
In long-term time series forecasting, different variables often influence the target variable over distinct time intervals, a challenge known as the multi-delay issue. Traditional models typically process all variables or time points uniformly, which limits their ability to capture complex variable relationships and obtain non-trivial time representations. To address this issue, we propose TimePro, an innovative Mamba-based model that constructs variate- and time-aware hyper-states. Unlike conventional approaches that merely transfer plain states across variable or time dimensions, TimePro preserves the fine-grained temporal features of each variate token and adaptively selects the focused time points to tune the plain state. The reconstructed hyper-state can perceive both variable relationships and salient temporal information, which helps the model make accurate forecasting. In experiments, TimePro performs competitively on eight real-world long-term forecasting benchmarks with satisfactory linear complexity. Code is available at https://github.com/xwmaxwma/TimePro.
Fund allocation has been an increasingly important problem in the financial domain. In reality, we aim to allocate the funds to buy certain assets within a certain future period. Naive solutions such as prediction-only or Predict-then-Optimize approaches suffer from goal mismatch. Additionally, the introduction of the SOTA time series forecasting model inevitably introduces additional uncertainty in the predicted result. To solve both problems mentioned above, we introduce a Risk-aware Time-Series Predict-and-Allocate (RTS-PnO) framework, which holds no prior assumption on the forecasting models. Such a framework contains three features: (i) end-to-end training with objective alignment measurement, (ii) adaptive forecasting uncertainty calibration, and (iii) agnostic towards forecasting models. The evaluation of RTS-PnO is conducted over both online and offline experiments. For offline experiments, eight datasets from three categories of financial applications are used: Currency, Stock, and Cryptos. RTS-PnO consistently outperforms other competitive baselines. The online experiment is conducted on the Cross-Border Payment business at FiT, Tencent, and an 8.4\% decrease in regret is witnessed when compared with the product-line approach. The code for the offline experiment is available at https://github.com/fuyuanlyu/RTS-PnO.
Time series forecasting (TSF) is a fundamental and widely studied task, spanning methods from classical statistical approaches to modern deep learning and multimodal language modeling. Despite their effectiveness, these methods often follow a fast thinking paradigm emphasizing pattern extraction and direct value mapping, while overlooking explicit reasoning over temporal dynamics and contextual dependencies. Meanwhile, emerging slow-thinking LLMs (e.g., ChatGPT-o1, DeepSeek-R1) have demonstrated impressive multi-step reasoning capabilities across diverse domains, suggesting a new opportunity for reframing TSF as a structured reasoning task. This motivates a key question: can slow-thinking LLMs effectively reason over temporal patterns to support time series forecasting, even in zero-shot manner? To investigate this, in this paper, we propose TimeReasoner, an extensive empirical study that formulates TSF as a conditional reasoning task. We design a series of prompting strategies to elicit inference-time reasoning from pretrained slow-thinking LLMs and evaluate their performance across diverse TSF benchmarks. Our findings reveal that slow-thinking LLMs exhibit non-trivial zero-shot forecasting capabilities, especially in capturing high-level trends and contextual shifts. While preliminary, our study surfaces important insights into the reasoning behaviors of LLMs in temporal domains highlighting both their potential and limitations. We hope this work catalyzes further research into reasoning-based forecasting paradigms and paves the way toward more interpretable and generalizable TSF frameworks.
In-context learning, the ability of large language models to perform tasks using only examples provided in the prompt, has recently been adapted for time series forecasting. This paradigm enables zero-shot prediction, where past values serve as context for forecasting future values, making powerful forecasting tools accessible to non-experts and increasing the performance when training data are scarce. Most existing zero-shot forecasting approaches rely on transformer architectures, which, despite their success in language, often fall short of expectations in time series forecasting, where recurrent models like LSTMs frequently have the edge. Conversely, while LSTMs are well-suited for time series modeling due to their state-tracking capabilities, they lack strong in-context learning abilities. We introduce TiRex that closes this gap by leveraging xLSTM, an enhanced LSTM with competitive in-context learning skills. Unlike transformers, state-space models, or parallelizable RNNs such as RWKV, TiRex retains state-tracking, a critical property for long-horizon forecasting. To further facilitate its state-tracking ability, we propose a training-time masking strategy called CPM. TiRex sets a new state of the art in zero-shot time series forecasting on the HuggingFace benchmarks GiftEval and Chronos-ZS, outperforming significantly larger models including TabPFN-TS (Prior Labs), Chronos Bolt (Amazon), TimesFM (Google), and Moirai (Salesforce) across both short- and long-term forecasts.
Time series forecasting with exogenous variables is a critical emerging paradigm that presents unique challenges in modeling dependencies between variables. Traditional models often struggle to differentiate between endogenous and exogenous variables, leading to inefficiencies and overfitting. In this paper, we introduce CrossLinear, a novel Linear-based forecasting model that addresses these challenges by incorporating a plug-and-play cross-correlation embedding module. This lightweight module captures the dependencies between variables with minimal computational cost and seamlessly integrates into existing neural networks. Specifically, it captures time-invariant and direct variable dependencies while disregarding time-varying or indirect dependencies, thereby mitigating the risk of overfitting in dependency modeling and contributing to consistent performance improvements. Furthermore, CrossLinear employs patch-wise processing and a global linear head to effectively capture both short-term and long-term temporal dependencies, further improving its forecasting precision. Extensive experiments on 12 real-world datasets demonstrate that CrossLinear achieves superior performance in both short-term and long-term forecasting tasks. The ablation study underscores the effectiveness of the cross-correlation embedding module. Additionally, the generalizability of this module makes it a valuable plug-in for various forecasting tasks across different domains. Codes are available at https://github.com/mumiao2000/CrossLinear.
Probabilistic Time Series Forecasting (PTSF) plays a crucial role in decision-making across various fields, including economics, energy, and transportation. Most existing methods excell at short-term forecasting, while overlooking the hurdles of Long-term Probabilistic Time Series Forecasting (LPTSF). As the forecast horizon extends, the inherent nonlinear dynamics have a significant adverse effect on prediction accuracy, and make generative models inefficient by increasing the cost of each iteration. To overcome these limitations, we introduce $K^2$VAE, an efficient VAE-based generative model that leverages a KoopmanNet to transform nonlinear time series into a linear dynamical system, and devises a KalmanNet to refine predictions and model uncertainty in such linear system, which reduces error accumulation in long-term forecasting. Extensive experiments demonstrate that $K^2$VAE outperforms state-of-the-art methods in both short- and long-term PTSF, providing a more efficient and accurate solution.
Time series forecasting remains a challenging task for foundation models due to temporal heterogeneity, high dimensionality, and the lack of inherent symbolic structure. In this work, we propose DRAGON (Discrete Representation and Augmented Graph encoding Over deBruijN Graphs), a novel encoder that introduces Multivariate de Bruijn Graphs (MdBGs) to bridge the gap between symbolic representations and neural modeling. DRAGON discretizes continuous input sequences and maps them onto a fixed graph structure, enabling dynamic context recovery via graph-based attention. Integrated as an auxiliary module within a dual-branch architecture, DRAGON augments conventional CNN-based encoders with symbolic, structure-aware representations. All code developed for this study is available at: https://github.com/KurbanIntelligenceLab/MultdBG-Time-Series-Library
The advent of universal time series forecasting models has revolutionized zero-shot forecasting across diverse domains, yet the critical role of data diversity in training these models remains underexplored. Existing large-scale time series datasets often suffer from inherent biases and imbalanced distributions, leading to suboptimal model performance and generalization. To address this gap, we introduce BLAST, a novel pre-training corpus designed to enhance data diversity through a balanced sampling strategy. First, BLAST incorporates 321 billion observations from publicly available datasets and employs a comprehensive suite of statistical metrics to characterize time series patterns. Then, to facilitate pattern-oriented sampling, the data is implicitly clustered using grid-based partitioning. Furthermore, by integrating grid sampling and grid mixup techniques, BLAST ensures a balanced and representative coverage of diverse patterns. Experimental results demonstrate that models pre-trained on BLAST achieve state-of-the-art performance with a fraction of the computational resources and training tokens required by existing methods. Our findings highlight the pivotal role of data diversity in improving both training efficiency and model performance for the universal forecasting task.
This paper introduces FANTF (Fuzzy Attention Network-Based Transformers), a novel approach that integrates fuzzy logic with existing transformer architectures to advance time series forecasting, classification, and anomaly detection tasks. FANTF leverages a proposed fuzzy attention mechanism incorporating fuzzy membership functions to handle uncertainty and imprecision in noisy and ambiguous time series data. The FANTF approach enhances its ability to capture complex temporal dependencies and multivariate relationships by embedding fuzzy logic principles into the self-attention module of the existing transformer's architecture. The framework combines fuzzy-enhanced attention with a set of benchmark existing transformer-based architectures to provide efficient predictions, classification and anomaly detection. Specifically, FANTF generates learnable fuzziness attention scores that highlight the relative importance of temporal features and data points, offering insights into its decision-making process. Experimental evaluatios on some real-world datasets reveal that FANTF significantly enhances the performance of forecasting, classification, and anomaly detection tasks over traditional transformer-based models.