Foundation Models for Time Series: A Survey

Transformer-based foundation models have emerged as a dominant paradigm in time series analysis, offering unprecedented capabilities in tasks such as forecasting, anomaly detection, classification, trend analysis and many more time series analytical tasks. This survey provides a comprehensive overview of the current state of the art pre-trained foundation models, introducing a novel taxonomy to categorize them across several dimensions. Specifically, we classify models by their architecture design, distinguishing between those leveraging patch-based representations and those operating directly on raw sequences. The taxonomy further includes whether the models provide probabilistic or deterministic predictions, and whether they are designed to work with univariate time series or can handle multivariate time series out of the box. Additionally, the taxonomy encompasses model scale and complexity, highlighting differences between lightweight architectures and large-scale foundation models. A unique aspect of this survey is its categorization by the type of objective function employed during training phase. By synthesizing these perspectives, this survey serves as a resource for researchers and practitioners, providing insights into current trends and identifying promising directions for future research in transformer-based time series modeling.

Dynamics and Computational Principles of Echo State Networks: A Mathematical Perspective

Reservoir computing (RC) represents a class of state-space models (SSMs) characterized by a fixed state transition mechanism (the reservoir) and a flexible readout layer that maps from the state space. It is a paradigm of computational dynamical systems that harnesses the transient dynamics of high-dimensional state spaces for efficient processing of temporal data. Rooted in concepts from recurrent neural networks, RC achieves exceptional computational power by decoupling the training of the dynamic reservoir from the linear readout layer, thereby circumventing the complexities of gradient-based optimization. This work presents a systematic exploration of RC, addressing its foundational properties such as the echo state property, fading memory, and reservoir capacity through the lens of dynamical systems theory. We formalize the interplay between input signals and reservoir states, demonstrating the conditions under which reservoirs exhibit stability and expressive power. Further, we delve into the computational trade-offs and robustness characteristics of RC architectures, extending the discussion to their applications in signal processing, time-series prediction, and control systems. The analysis is complemented by theoretical insights into optimization, training methodologies, and scalability, highlighting open challenges and potential directions for advancing the theoretical underpinnings of RC.

Exploring the Effectiveness and Interpretability of Texts in LLM-based Time Series Models

Large Language Models (LLMs) have been applied to time series forecasting tasks, leveraging pre-trained language models as the backbone and incorporating textual data to purportedly enhance the comprehensive capabilities of LLMs for time series. However, are these texts really helpful for interpretation? This study seeks to investigate the actual efficacy and interpretability of such textual incorporations. Through a series of empirical experiments on textual prompts and textual prototypes, our findings reveal that the misalignment between two modalities exists, and the textual information does not significantly improve time series forecasting performance in many cases. Furthermore, visualization analysis indicates that the textual representations learned by existing frameworks lack sufficient interpretability when applied to time series data. We further propose a novel metric named Semantic Matching Index (SMI) to better evaluate the matching degree between time series and texts during our post hoc interpretability investigation. Our analysis reveals the misalignment and limited interpretability of texts in current time-series LLMs, and we hope this study can raise awareness of the interpretability of texts for time series. The code is available at https://github.com/zachysun/TS-Lang-Exp.

Interval-Valued Time Series Classification Using $D_K$-Distance

In recent years, modeling and analysis of interval-valued time series have garnered increasing attention in econometrics, finance, and statistics. However, these studies have predominantly focused on statistical inference in the forecasting of univariate and multivariate interval-valued time series, overlooking another important aspect: classification. In this paper, we introduce a classification approach that treats intervals as unified entities, applicable to both univariate and multivariate interval-valued time series. Specifically, we first extend the point-valued time series imaging methods to interval-valued scenarios using the $D_K$-distance, enabling the imaging of interval-valued time series. Then, we employ suitable deep learning model for classification on the obtained imaging dataset, aiming to achieve classification for interval-valued time series. In theory, we derived a sharper excess risk bound for deep multiclassifiers based on offset Rademacher complexity. Finally, we validate the superiority of the proposed method through comparisons with various existing point-valued time series classification methods in both simulation studies and real data applications.

An Analysis of Temporal Dropout in Earth Observation Time Series for Regression Tasks

Missing instances in time series data impose a significant challenge to deep learning models, particularly in regression tasks. In the Earth Observation field, satellite failure or cloud occlusion frequently results in missing time-steps, introducing uncertainties in the predicted output and causing a decline in predictive performance. While many studies address missing time-steps through data augmentation to improve model robustness, the uncertainty arising at the input level is commonly overlooked. To address this gap, we introduce Monte Carlo Temporal Dropout (MC-TD), a method that explicitly accounts for input-level uncertainty by randomly dropping time-steps during inference using a predefined dropout ratio, thereby simulating the effect of missing data. To bypass the need for costly searches for the optimal dropout ratio, we extend this approach with Monte Carlo Concrete Temporal Dropout (MC-ConcTD), a method that learns the optimal dropout distribution directly. Both MC-TD and MC-ConcTD are applied during inference, leveraging Monte Carlo sampling for uncertainty quantification. Experiments on three EO time-series datasets demonstrate that MC-ConcTD improves predictive performance and uncertainty calibration compared to existing approaches. Additionally, we highlight the advantages of adaptive dropout tuning over manual selection, making uncertainty quantification more robust and accessible for EO applications.

TSP-OCS: A Time-Series Prediction for Optimal Camera Selection in Multi-Viewpoint Surgical Video Analysis

Recording the open surgery process is essential for educational and medical evaluation purposes; however, traditional single-camera methods often face challenges such as occlusions caused by the surgeon's head and body, as well as limitations due to fixed camera angles, which reduce comprehensibility of the video content. This study addresses these limitations by employing a multi-viewpoint camera recording system, capturing the surgical procedure from six different angles to mitigate occlusions. We propose a fully supervised learning-based time series prediction method to choose the best shot sequences from multiple simultaneously recorded video streams, ensuring optimal viewpoints at each moment. Our time series prediction model forecasts future camera selections by extracting and fusing visual and semantic features from surgical videos using pre-trained models. These features are processed by a temporal prediction network with TimeBlocks to capture sequential dependencies. A linear embedding layer reduces dimensionality, and a Softmax classifier selects the optimal camera view based on the highest probability. In our experiments, we created five groups of open thyroidectomy videos, each with simultaneous recordings from six different angles. The results demonstrate that our method achieves competitive accuracy compared to traditional supervised methods, even when predicting over longer time horizons. Furthermore, our approach outperforms state-of-the-art time series prediction techniques on our dataset. This manuscript makes a unique contribution by presenting an innovative framework that advances surgical video analysis techniques, with significant implications for improving surgical education and patient safety.

Adaptive Classification of Interval-Valued Time Series

In recent years, the modeling and analysis of interval-valued time series have garnered significant attention in the fields of econometrics and statistics. However, the existing literature primarily focuses on regression tasks while neglecting classification aspects. In this paper, we propose an adaptive approach for interval-valued time series classification. Specifically, we represent interval-valued time series using convex combinations of upper and lower bounds of intervals and transform these representations into images based on point-valued time series imaging methods. We utilize a fine-grained image classification neural network to classify these images, to achieve the goal of classifying the original interval-valued time series. This proposed method is applicable to both univariate and multivariate interval-valued time series. On the optimization front, we treat the convex combination coefficients as learnable parameters similar to the parameters of the neural network and provide an efficient estimation method based on the alternating direction method of multipliers (ADMM). On the theoretical front, under specific conditions, we establish a margin-based multiclass generalization bound for generic CNNs composed of basic blocks involving convolution, pooling, and fully connected layers. Through simulation studies and real data applications, we validate the effectiveness of the proposed method and compare its performance against a wide range of point-valued time series classification methods.

Forecasting from Clinical Textual Time Series: Adaptations of the Encoder and Decoder Language Model Families

Clinical case reports encode rich, temporal patient trajectories that are often underexploited by traditional machine learning methods relying on structured data. In this work, we introduce the forecasting problem from textual time series, where timestamped clinical findings--extracted via an LLM-assisted annotation pipeline--serve as the primary input for prediction. We systematically evaluate a diverse suite of models, including fine-tuned decoder-based large language models and encoder-based transformers, on tasks of event occurrence prediction, temporal ordering, and survival analysis. Our experiments reveal that encoder-based models consistently achieve higher F1 scores and superior temporal concordance for short- and long-horizon event forecasting, while fine-tuned masking approaches enhance ranking performance. In contrast, instruction-tuned decoder models demonstrate a relative advantage in survival analysis, especially in early prognosis settings. Our sensitivity analyses further demonstrate the importance of time ordering, which requires clinical time series construction, as compared to text ordering, the format of the text inputs that LLMs are classically trained on. This highlights the additional benefit that can be ascertained from time-ordered corpora, with implications for temporal tasks in the era of widespread LLM use.

Entropic Analysis of Time Series through Kernel Density Estimation

This work presents a novel framework for time series analysis using entropic measures based on the kernel density estimate (KDE) of the time series' Takens' embeddings. Using this framework we introduce two distinct analytical tools: (1) a multi-scale KDE entropy metric, denoted as $\Delta\text{KE}$, which quantifies the evolution of time series complexity across different scales by measuring certain entropy changes, and (2) a sliding baseline method that employs the Kullback-Leibler (KL) divergence to detect changes in time series dynamics through changes in KDEs. The $\Delta{\rm KE}$ metric offers insights into the information content and ``unfolding'' properties of the time series' embedding related to dynamical systems, while the KL divergence-based approach provides a noise and outlier robust approach for identifying time series change points (injections in RF signals, e.g.). We demonstrate the versatility and effectiveness of these tools through a set of experiments encompassing diverse domains. In the space of radio frequency (RF) signal processing, we achieve accurate detection of signal injections under varying noise and interference conditions. Furthermore, we apply our methodology to electrocardiography (ECG) data, successfully identifying instances of ventricular fibrillation with high accuracy. Finally, we demonstrate the potential of our tools for dynamic state detection by accurately identifying chaotic regimes within an intermittent signal. These results show the broad applicability of our framework for extracting meaningful insights from complex time series data across various scientific disciplines.

Ethereum Price Prediction Employing Large Language Models for Short-term and Few-shot Forecasting

Cryptocurrencies have transformed financial markets with their innovative blockchain technology and volatile price movements, presenting both challenges and opportunities for predictive analytics. Ethereum, being one of the leading cryptocurrencies, has experienced significant market fluctuations, making its price prediction an attractive yet complex problem. This paper presents a comprehensive study on the effectiveness of Large Language Models (LLMs) in predicting Ethereum prices for short-term and few-shot forecasting scenarios. The main challenge in training models for time series analysis is the lack of data. We address this by leveraging a novel approach that adapts existing pre-trained LLMs on natural language or images from billions of tokens to the unique characteristics of Ethereum price time series data. Through thorough experimentation and comparison with traditional and contemporary models, our results demonstrate that selectively freezing certain layers of pre-trained LLMs achieves state-of-the-art performance in this domain. This approach consistently surpasses benchmarks across multiple metrics, including Mean Squared Error (MSE), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE), demonstrating its effectiveness and robustness. Our research not only contributes to the existing body of knowledge on LLMs but also provides practical insights in the cryptocurrency prediction domain. The adaptability of pre-trained LLMs to handle the nature of Ethereum prices suggests a promising direction for future research, potentially including the integration of sentiment analysis to further refine forecasting accuracy.