Counterfactual Explanation for Multivariate Time Series Forecasting with Exogenous Variables

Currently, machine learning is widely used across various domains, including time series data analysis. However, some machine learning models function as black boxes, making interpretability a critical concern. One approach to address this issue is counterfactual explanation (CE), which aims to provide insights into model predictions. This study focuses on the relatively underexplored problem of generating counterfactual explanations for time series forecasting. We propose a method for extracting CEs in time series forecasting using exogenous variables, which are frequently encountered in fields such as business and marketing. In addition, we present methods for analyzing the influence of each variable over an entire time series, generating CEs by altering only specific variables, and evaluating the quality of the resulting CEs. We validate the proposed method through theoretical analysis and empirical experiments, showcasing its accuracy and practical applicability. These contributions are expected to support real-world decision-making based on time series data analysis.

STAMP: Spatial-Temporal Adapter with Multi-Head Pooling

Time series foundation models (TSFMs) pretrained on data from multiple domains have shown strong performance on diverse modeling tasks. Various efforts have been made to develop foundation models specific to electroencephalography (EEG) data, which records brain electrical activity as time series. However, no comparative analysis of EEG-specific foundation models (EEGFMs) versus general TSFMs has been performed on EEG-specific tasks. We introduce a novel Spatial-Temporal Adapter with Multi-Head Pooling (STAMP), which leverages univariate embeddings produced by a general TSFM, implicitly models spatial-temporal characteristics of EEG data, and achieves performance comparable to state-of-the-art EEGFMs. A comprehensive analysis is performed on 8 benchmark datasets of clinical tasks using EEG for classification, along with ablation studies. Our proposed adapter is lightweight in trainable parameters and flexible in the inputs it can accommodate, supporting easy modeling of EEG data using TSFMs.

Reasoning on Time-Series for Financial Technical Analysis

While Large Language Models have been used to produce interpretable stock forecasts, they mainly focus on analyzing textual reports but not historical price data, also known as Technical Analysis. This task is challenging as it switches between domains: the stock price inputs and outputs lie in the time-series domain, while the reasoning step should be in natural language. In this work, we introduce Verbal Technical Analysis (VTA), a novel framework that combine verbal and latent reasoning to produce stock time-series forecasts that are both accurate and interpretable. To reason over time-series, we convert stock price data into textual annotations and optimize the reasoning trace using an inverse Mean Squared Error (MSE) reward objective. To produce time-series outputs from textual reasoning, we condition the outputs of a time-series backbone model on the reasoning-based attributes. Experiments on stock datasets across U.S., Chinese, and European markets show that VTA achieves state-of-the-art forecasting accuracy, while the reasoning traces also perform well on evaluation by industry experts.

A Theoretical Analysis of Detecting Large Model-Generated Time Series

Motivated by the increasing risks of data misuse and fabrication, we investigate the problem of identifying synthetic time series generated by Time-Series Large Models (TSLMs) in this work. While there are extensive researches on detecting model generated text, we find that these existing methods are not applicable to time series data due to the fundamental modality difference, as time series usually have lower information density and smoother probability distributions than text data, which limit the discriminative power of token-based detectors. To address this issue, we examine the subtle distributional differences between real and model-generated time series and propose the contraction hypothesis, which states that model-generated time series, unlike real ones, exhibit progressively decreasing uncertainty under recursive forecasting. We formally prove this hypothesis under theoretical assumptions on model behavior and time series structure. Model-generated time series exhibit progressively concentrated distributions under recursive forecasting, leading to uncertainty contraction. We provide empirical validation of the hypothesis across diverse datasets. Building on this insight, we introduce the Uncertainty Contraction Estimator (UCE), a white-box detector that aggregates uncertainty metrics over successive prefixes to identify TSLM-generated time series. Extensive experiments on 32 datasets show that UCE consistently outperforms state-of-the-art baselines, offering a reliable and generalizable solution for detecting model-generated time series.

Optimal Look-back Horizon for Time Series Forecasting in Federated Learning

Selecting an appropriate look-back horizon remains a fundamental challenge in time series forecasting (TSF), particularly in the federated learning scenarios where data is decentralized, heterogeneous, and often non-independent. While recent work has explored horizon selection by preserving forecasting-relevant information in an intrinsic space, these approaches are primarily restricted to centralized and independently distributed settings. This paper presents a principled framework for adaptive horizon selection in federated time series forecasting through an intrinsic space formulation. We introduce a synthetic data generator (SDG) that captures essential temporal structures in client data, including autoregressive dependencies, seasonality, and trend, while incorporating client-specific heterogeneity. Building on this model, we define a transformation that maps time series windows into an intrinsic representation space with well-defined geometric and statistical properties. We then derive a decomposition of the forecasting loss into a Bayesian term, which reflects irreducible uncertainty, and an approximation term, which accounts for finite-sample effects and limited model capacity. Our analysis shows that while increasing the look-back horizon improves the identifiability of deterministic patterns, it also increases approximation error due to higher model complexity and reduced sample efficiency. We prove that the total forecasting loss is minimized at the smallest horizon where the irreducible loss starts to saturate, while the approximation loss continues to rise. This work provides a rigorous theoretical foundation for adaptive horizon selection for time series forecasting in federated learning.

Spectral Predictability as a Fast Reliability Indicator for Time Series Forecasting Model Selection

Practitioners deploying time series forecasting models face a dilemma: exhaustively validating dozens of models is computationally prohibitive, yet choosing the wrong model risks poor performance. We show that spectral predictability~$Ω$ -- a simple signal processing metric -- systematically stratifies model family performance, enabling fast model selection. We conduct controlled experiments in four different domains, then further expand our analysis to 51 models and 28 datasets from the GIFT-Eval benchmark. We find that large time series foundation models (TSFMs) systematically outperform lightweight task-trained baselines when $Ω$ is high, while their advantage vanishes as $Ω$ drops. Computing $Ω$ takes seconds per dataset, enabling practitioners to quickly assess whether their data suits TSFM approaches or whether simpler, cheaper models suffice. We demonstrate that $Ω$ stratifies model performance predictably, offering a practical first-pass filter that reduces validation costs while highlighting the need for models that excel on genuinely difficult (low-$Ω$) problems rather than merely optimizing easy ones.

MedFuse: Multiplicative Embedding Fusion For Irregular Clinical Time Series

Clinical time series derived from electronic health records (EHRs) are inherently irregular, with asynchronous sampling, missing values, and heterogeneous feature dynamics. While numerical laboratory measurements are highly informative, existing embedding strategies usually combine feature identity and value embeddings through additive operations, which constrains their ability to capture value-dependent feature interactions. We propose MedFuse, a framework for irregular clinical time series centered on the MuFuse (Multiplicative Embedding Fusion) module. MuFuse fuses value and feature embeddings through multiplicative modulation, preserving feature-specific information while modeling higher-order dependencies across features. Experiments on three real-world datasets covering both intensive and chronic care show that MedFuse consistently outperforms state-of-the-art baselines on key predictive tasks. Analysis of the learned representations further demonstrates that multiplicative fusion enhances expressiveness and supports cross-dataset pretraining. These results establish MedFuse as a generalizable approach for modeling irregular clinical time series.

Multivariate Time series Anomaly Detection:A Framework of Hidden Markov Models

In this study, we develop an approach to multivariate time series anomaly detection focused on the transformation of multivariate time series to univariate time series. Several transformation techniques involving Fuzzy C-Means (FCM) clustering and fuzzy integral are studied. In the sequel, a Hidden Markov Model (HMM), one of the commonly encountered statistical methods, is engaged here to detect anomalies in multivariate time series. We construct HMM-based anomaly detectors and in this context compare several transformation methods. A suite of experimental studies along with some comparative analysis is reported.

Towards Causal Market Simulators

Market generators using deep generative models have shown promise for synthetic financial data generation, but existing approaches lack causal reasoning capabilities essential for counterfactual analysis and risk assessment. We propose a Time-series Neural Causal Model VAE (TNCM-VAE) that combines variational autoencoders with structural causal models to generate counterfactual financial time series while preserving both temporal dependencies and causal relationships. Our approach enforces causal constraints through directed acyclic graphs in the decoder architecture and employs the causal Wasserstein distance for training. We validate our method on synthetic autoregressive models inspired by the Ornstein-Uhlenbeck process, demonstrating superior performance in counterfactual probability estimation with L1 distances as low as 0.03-0.10 compared to ground truth. The model enables financial stress testing, scenario analysis, and enhanced backtesting by generating plausible counterfactual market trajectories that respect underlying causal mechanisms.

MAP4TS: A Multi-Aspect Prompting Framework for Time-Series Forecasting with Large Language Models

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.