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Time series analysis comprises statistical methods for analyzing a sequence of data points collected over an interval of time to identify interesting patterns and trends.
Papers and Code
MAP4TS: A Multi-Aspect Prompting Framework for Time-Series Forecasting with Large Language Models
Oct 27, 2025
Recent advances have investigated the use of pretrained large language models (LLMs) for time-series forecasting by aligning numerical inputs with LLM embedding spaces. However, existing multimodal approaches often overlook the distinct statistical properties and temporal dependencies that are fundamental to time-series data. To bridge this gap, we propose MAP4TS, a novel Multi-Aspect Prompting Framework that explicitly incorporates classical time-series analysis into the prompt design. Our framework introduces four specialized prompt components: a Global Domain Prompt that conveys dataset-level context, a Local Domain Prompt that encodes recent trends and series-specific behaviors, and a pair of Statistical and Temporal Prompts that embed handcrafted insights derived from autocorrelation (ACF), partial autocorrelation (PACF), and Fourier analysis. Multi-Aspect Prompts are combined with raw time-series embeddings and passed through a cross-modality alignment module to produce unified representations, which are then processed by an LLM and projected for final forecasting. Extensive experiments across eight diverse datasets show that MAP4TS consistently outperforms state-of-the-art LLM-based methods. Our ablation studies further reveal that prompt-aware designs significantly enhance performance stability and that GPT-2 backbones, when paired with structured prompts, outperform larger models like LLaMA in long-term forecasting tasks.
Rmd: Robust Modal Decomposition with Constrained Bandwidth
Oct 27, 2025Modal decomposition techniques, such as Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Singular Spectrum Analysis (SSA), have advanced time-frequency signal analysis since the early 21st century. These methods are generally classified into two categories: numerical optimization-based methods (EMD, VMD) and spectral decomposition methods (SSA) that consider the physical meaning of signals. The former can produce spurious modes due to the lack of physical constraints, while the latter is more sensitive to noise and struggles with nonlinear signals. Despite continuous improvements in these methods, a modal decomposition approach that effectively combines the strengths of both categories remains elusive. This paper thus proposes a Robust Modal Decomposition (RMD) method with constrained bandwidth, which preserves the intrinsic structure of the signal by mapping the time series into its trajectory-GRAM matrix in phase space. Moreover, the method incorporates bandwidth constraints during the decomposition process, enhancing noise resistance. Extensive experiments on synthetic and real-world datasets, including millimeter-wave radar echoes, electrocardiogram (ECG), phonocardiogram (PCG), and bearing fault detection data, demonstrate the method's effectiveness and versatility. All code and dataset samples are available on GitHub: https://github.com/Einstein-sworder/RMD.
Benchmarking Catastrophic Forgetting Mitigation Methods in Federated Time Series Forecasting
Oct 24, 2025Catastrophic forgetting (CF) poses a persistent challenge in continual learning (CL), especially within federated learning (FL) environments characterized by non-i.i.d. time series data. While existing research has largely focused on classification tasks in vision domains, the regression-based forecasting setting prevalent in IoT and edge applications remains underexplored. In this paper, we present the first benchmarking framework tailored to investigate CF in federated continual time series forecasting. Using the Beijing Multi-site Air Quality dataset across 12 decentralized clients, we systematically evaluate several CF mitigation strategies, including Replay, Elastic Weight Consolidation, Learning without Forgetting, and Synaptic Intelligence. Key contributions include: (i) introducing a new benchmark for CF in time series FL, (ii) conducting a comprehensive comparative analysis of state-of-the-art methods, and (iii) releasing a reproducible open-source framework. This work provides essential tools and insights for advancing continual learning in federated time-series forecasting systems.
Unsupervised Anomaly Prediction with N-BEATS and Graph Neural Network in Multi-variate Semiconductor Process Time Series
Oct 23, 2025Semiconductor manufacturing is an extremely complex and precision-driven process, characterized by thousands of interdependent parameters collected across diverse tools and process steps. Multi-variate time-series analysis has emerged as a critical field for real-time monitoring and fault detection in such environments. However, anomaly prediction in semiconductor fabrication presents several critical challenges, including high dimensionality of sensor data and severe class imbalance due to the rarity of true faults. Furthermore, the complex interdependencies between variables complicate both anomaly prediction and root-cause-analysis. This paper proposes two novel approaches to advance the field from anomaly detection to anomaly prediction, an essential step toward enabling real-time process correction and proactive fault prevention. The proposed anomaly prediction framework contains two main stages: (a) training a forecasting model on a dataset assumed to contain no anomalies, and (b) performing forecast on unseen time series data. The forecast is compared with the forecast of the trained signal. Deviations beyond a predefined threshold are flagged as anomalies. The two approaches differ in the forecasting model employed. The first assumes independence between variables by utilizing the N-BEATS model for univariate time series forecasting. The second lifts this assumption by utilizing a Graph Neural Network (GNN) to capture inter-variable relationships. Both models demonstrate strong forecasting performance up to a horizon of 20 time points and maintain stable anomaly prediction up to 50 time points. The GNN consistently outperforms the N-BEATS model while requiring significantly fewer trainable parameters and lower computational cost. These results position the GNN as promising solution for online anomaly forecasting to be deployed in manufacturing environments.
No Intelligence Without Statistics: The Invisible Backbone of Artificial Intelligence
Oct 22, 2025The rapid ascent of artificial intelligence (AI) is often portrayed as a revolution born from computer science and engineering. This narrative, however, obscures a fundamental truth: the theoretical and methodological core of AI is, and has always been, statistical. This paper systematically argues that the field of statistics provides the indispensable foundation for machine learning and modern AI. We deconstruct AI into nine foundational pillars-Inference, Density Estimation, Sequential Learning, Generalization, Representation Learning, Interpretability, Causality, Optimization, and Unification-demonstrating that each is built upon century-old statistical principles. From the inferential frameworks of hypothesis testing and estimation that underpin model evaluation, to the density estimation roots of clustering and generative AI; from the time-series analysis inspiring recurrent networks to the causal models that promise true understanding, we trace an unbroken statistical lineage. While celebrating the computational engines that power modern AI, we contend that statistics provides the brain-the theoretical frameworks, uncertainty quantification, and inferential goals-while computer science provides the brawn-the scalable algorithms and hardware. Recognizing this statistical backbone is not merely an academic exercise, but a necessary step for developing more robust, interpretable, and trustworthy intelligent systems. We issue a call to action for education, research, and practice to re-embrace this statistical foundation. Ignoring these roots risks building a fragile future; embracing them is the path to truly intelligent machines. There is no machine learning without statistical learning; no artificial intelligence without statistical thought.
Topology of Currencies: Persistent Homology for FX Co-movements: A Comparative Clustering Study
Oct 22, 2025This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviours. We focus on the foreign exchange (FX) market, which is a complex system often exhibiting non-linear and high-dimensional dynamics that classical techniques may not fully capture. We compare clustering results based on TDA-derived features versus classical statistical features using monthly logarithmic returns of 13 major currency exchange rates (all against the euro). Two widely-used clustering algorithms, \(k\)-means and Hierarchical clustering, are applied on both types of features, and cluster quality is evaluated via the Silhouette score and the Calinski-Harabasz index. Our findings show that TDA-based feature clustering produces more compact and well-separated clusters than clustering on traditional statistical features, particularly achieving substantially higher Calinski-Harabasz scores. However, all clustering approaches yield modest Silhouette scores, underscoring the inherent difficulty of grouping FX time series. The differing cluster compositions under TDA vs. classical features suggest that TDA captures structural patterns in currency co-movements that conventional methods might overlook. These results highlight TDA as a valuable complementary tool for analysing financial time series, with potential applications in risk management where understanding structural co-movements is crucial.
Generalist vs Specialist Time Series Foundation Models: Investigating Potential Emergent Behaviors in Assessing Human Health Using PPG Signals
Oct 16, 2025Foundation models are large-scale machine learning models that are pre-trained on massive amounts of data and can be adapted for various downstream tasks. They have been extensively applied to tasks in Natural Language Processing and Computer Vision with models such as GPT, BERT, and CLIP. They are now also increasingly gaining attention in time-series analysis, particularly for physiological sensing. However, most time series foundation models are specialist models - with data in pre-training and testing of the same type, such as Electrocardiogram, Electroencephalogram, and Photoplethysmogram (PPG). Recent works, such as MOMENT, train a generalist time series foundation model with data from multiple domains, such as weather, traffic, and electricity. This paper aims to conduct a comprehensive benchmarking study to compare the performance of generalist and specialist models, with a focus on PPG signals. Through an extensive suite of total 51 tasks covering cardiac state assessment, laboratory value estimation, and cross-modal inference, we comprehensively evaluate both models across seven dimensions, including win score, average performance, feature quality, tuning gain, performance variance, transferability, and scalability. These metrics jointly capture not only the models' capability but also their adaptability, robustness, and efficiency under different fine-tuning strategies, providing a holistic understanding of their strengths and limitations for diverse downstream scenarios. In a full-tuning scenario, we demonstrate that the specialist model achieves a 27% higher win score. Finally, we provide further analysis on generalization, fairness, attention visualizations, and the importance of training data choice.
TENDE: Transfer Entropy Neural Diffusion Estimation
Oct 15, 2025Transfer entropy measures directed information flow in time series, and it has become a fundamental quantity in applications spanning neuroscience, finance, and complex systems analysis. However, existing estimation methods suffer from the curse of dimensionality, require restrictive distributional assumptions, or need exponentially large datasets for reliable convergence. We address these limitations in the literature by proposing TENDE (Transfer Entropy Neural Diffusion Estimation), a novel approach that leverages score-based diffusion models to estimate transfer entropy through conditional mutual information. By learning score functions of the relevant conditional distributions, TENDE provides flexible, scalable estimation while making minimal assumptions about the underlying data-generating process. We demonstrate superior accuracy and robustness compared to existing neural estimators and other state-of-the-art approaches across synthetic benchmarks and real data.
On Evaluating Loss Functions for Stock Ranking: An Empirical Analysis With Transformer Model
Oct 15, 2025Quantitative trading strategies rely on accurately ranking stocks to identify profitable investments. Effective portfolio management requires models that can reliably order future stock returns. Transformer models are promising for understanding financial time series, but how different training loss functions affect their ability to rank stocks well is not yet fully understood. Financial markets are challenging due to their changing nature and complex relationships between stocks. Standard loss functions, which aim for simple prediction accuracy, often aren't enough. They don't directly teach models to learn the correct order of stock returns. While many advanced ranking losses exist from fields such as information retrieval, there hasn't been a thorough comparison to see how well they work for ranking financial returns, especially when used with modern Transformer models for stock selection. This paper addresses this gap by systematically evaluating a diverse set of advanced loss functions including pointwise, pairwise, listwise for daily stock return forecasting to facilitate rank-based portfolio selection on S&P 500 data. We focus on assessing how each loss function influences the model's ability to discern profitable relative orderings among assets. Our research contributes a comprehensive benchmark revealing how different loss functions impact a model's ability to learn cross-sectional and temporal patterns crucial for portfolio selection, thereby offering practical guidance for optimizing ranking-based trading strategies.
Vacuum Spiker: A Spiking Neural Network-Based Model for Efficient Anomaly Detection in Time Series
Oct 08, 2025
Anomaly detection is a key task across domains such as industry, healthcare, and cybersecurity. Many real-world anomaly detection problems involve analyzing multiple features over time, making time series analysis a natural approach for such problems. While deep learning models have achieved strong performance in this field, their trend to exhibit high energy consumption limits their deployment in resource-constrained environments such as IoT devices, edge computing platforms, and wearables. To address this challenge, this paper introduces the \textit{Vacuum Spiker algorithm}, a novel Spiking Neural Network-based method for anomaly detection in time series. It incorporates a new detection criterion that relies on global changes in neural activity rather than reconstruction or prediction error. It is trained using Spike Time-Dependent Plasticity in a novel way, intended to induce changes in neural activity when anomalies occur. A new efficient encoding scheme is also proposed, which discretizes the input space into non-overlapping intervals, assigning each to a single neuron. This strategy encodes information with a single spike per time step, improving energy efficiency compared to conventional encoding methods. Experimental results on publicly available datasets show that the proposed algorithm achieves competitive performance while significantly reducing energy consumption, compared to a wide set of deep learning and machine learning baselines. Furthermore, its practical utility is validated in a real-world case study, where the model successfully identifies power curtailment events in a solar inverter. These results highlight its potential for sustainable and efficient anomaly detection.