FreqCycle: A Multi-Scale Time-Frequency Analysis Method for Time Series Forecasting

Mining time-frequency features is critical for time series forecasting. Existing research has predominantly focused on modeling low-frequency patterns, where most time series energy is concentrated. The overlooking of mid to high frequency continues to limit further performance gains in deep learning models. We propose FreqCycle, a novel framework integrating: (i) a Filter-Enhanced Cycle Forecasting (FECF) module to extract low-frequency features by explicitly learning shared periodic patterns in the time domain, and (ii) a Segmented Frequency-domain Pattern Learning (SFPL) module to enhance mid to high frequency energy proportion via learnable filters and adaptive weighting. Furthermore, time series data often exhibit coupled multi-periodicity, such as intertwined weekly and daily cycles. To address coupled multi-periodicity as well as long lookback window challenges, we extend FreqCycle hierarchically into MFreqCycle, which decouples nested periodic features through cross-scale interactions. Extensive experiments on seven diverse domain benchmarks demonstrate that FreqCycle achieves state-of-the-art accuracy while maintaining faster inference speeds, striking an optimal balance between performance and efficiency.

Revisiting OmniAnomaly for Anomaly Detection: performance metrics and comparison with PCA-based models

Deep learning models have become the dominant approach for multivariate time series anomaly detection (MTSAD), often reporting substantial performance improvements over classical statistical methods. However, these gains are frequently evaluated under heterogeneous thresholding strategies and evaluation protocols, making fair comparisons difficult. This work revisits OmniAnomaly, a widely used stochastic recurrent model for MTSAD, and systematically compares it with a simple linear baseline based on Principal Component Analysis (PCA) on the Server Machine Dataset (SMD). Both methods are evaluated under identical thresholding and evaluation procedures, with experiments repeated across 100 runs for each of the 28 machines in the dataset. Performance is evaluated using Precision, Recall and F1-score at point-level, with and without point-adjustment, and under different aggregation strategies across machines and runs, with the corresponding standard deviations also reported. The results show large variability across machines and show that PCA can achieve performance comparable to OmniAnomaly, and even outperform it when point-adjustment is not applied. These findings question the added value of more complex architectures under current benchmarking practices and highlight the critical role of evaluation methodology in MTSAD research.

Unified Taxonomy for Multivariate Time Series Anomaly Detection using Deep Learning

The topic of Multivariate Time Series Anomaly Detection (MTSAD) has grown rapidly over the past years, with a steady rise in publications and Deep Learning (DL) models becoming the dominant paradigm. To address the lack of systematization in the field, this study introduces a novel and unified taxonomy with eleven dimensions over three parts (Input, Output and Model) for the categorization of DL-based MTSAD methods. The dimensions were established in a two-fold approach. First, they derived from a comprehensive analysis of methodological studies. Second, insights from review papers were incorporated. Furthermore, the proposed taxonomy was validated using an additional set of recent publications, providing a clear overview of methodological trends in MTSAD. Results reveal a convergence toward Transformer-based and reconstruction and prediction models, setting the foundation for emerging adaptive and generative trends. Building on and complementing existing surveys, this unified taxonomy is designed to accommodate future developments, allowing for new categories or dimensions to be added as the field progresses. This work thus consolidates fragmented knowledge in the field and provides a reference point for future research in MTSAD.

The Density of Cross-Persistence Diagrams and Its Applications

Topological Data Analysis (TDA) provides powerful tools to explore the shape and structure of data through topological features such as clusters, loops, and voids. Persistence diagrams are a cornerstone of TDA, capturing the evolution of these features across scales. While effective for analyzing individual manifolds, persistence diagrams do not account for interactions between pairs of them. Cross-persistence diagrams (cross-barcodes), introduced recently, address this limitation by characterizing relationships between topological features of two point clouds. In this work, we present the first systematic study of the density of cross-persistence diagrams. We prove its existence, establish theoretical foundations for its statistical use, and design the first machine learning framework for predicting cross-persistence density directly from point cloud coordinates and distance matrices. Our statistical approach enables the distinction of point clouds sampled from different manifolds by leveraging the linear characteristics of cross-persistence diagrams. Interestingly, we find that introducing noise can enhance our ability to distinguish point clouds, uncovering its novel utility in TDA applications. We demonstrate the effectiveness of our methods through experiments on diverse datasets, where our approach consistently outperforms existing techniques in density prediction and achieves superior results in point cloud distinction tasks. Our findings contribute to a broader understanding of cross-persistence diagrams and open new avenues for their application in data analysis, including potential insights into time-series domain tasks and the geometry of AI-generated texts. Our code is publicly available at https://github.com/Verdangeta/TDA_experiments

Ultra-Early Prediction of Tipping Points: Integrating Dynamical Measures with Reservoir Computing

Complex dynamical systems-such as climate, ecosystems, and economics-can undergo catastrophic and potentially irreversible regime changes, often triggered by environmental parameter drift and stochastic disturbances. These critical thresholds, known as tipping points, pose a prediction problem of both theoretical and practical significance, yet remain largely unresolved. To address this, we articulate a model-free framework that integrates the measures characterizing the stability and sensitivity of dynamical systems with the reservoir computing (RC), a lightweight machine learning technique, using only observational time series data. The framework consists of two stages. The first stage involves using RC to robustly learn local complex dynamics from observational data segmented into windows. The second stage focuses on accurately detecting early warning signals of tipping points by analyzing the learned autonomous RC dynamics through dynamical measures, including the dominant eigenvalue of the Jacobian matrix, the maximum Floquet multiplier, and the maximum Lyapunov exponent. Furthermore, when these dynamical measures exhibit trend-like patterns, their extrapolation enables ultra-early prediction of tipping points significantly prior to the occurrence of critical transitions. We conduct a rigorous theoretical analysis of the proposed method and perform extensive numerical evaluations on a series of representative synthetic systems and eight real-world datasets, as well as quantitatively predict the tipping time of the Atlantic Meridional Overturning Circulation system. Experimental results demonstrate that our framework exhibits advantages over the baselines in comprehensive evaluations, particularly in terms of dynamical interpretability, prediction stability and robustness, and ultra-early prediction capability.

Spatio-Temporal Grid Intelligence: A Hybrid Graph Neural Network and LSTM Framework for Robust Electricity Theft Detection

Electricity theft, or non-technical loss (NTL), presents a persistent threat to global power systems, driving significant financial deficits and compromising grid stability. Conventional detection methodologies, predominantly reactive and meter-centric, often fail to capture the complex spatio-temporal dynamics and behavioral patterns associated with fraudulent consumption. This study introduces a novel AI-driven Grid Intelligence Framework that fuses Time-Series Anomaly Detection, Supervised Machine Learning, and Graph Neural Networks (GNN) to identify theft with high precision in imbalanced datasets. Leveraging an enriched feature set, including rolling averages, voltage drop estimates, and a critical Grid Imbalance Index, the methodology employs a Long Short-Term Memory (LSTM) autoencoder for temporal anomaly scoring, a Random Forest classifier for tabular feature discrimination, and a GNN to model spatial dependencies across the distribution network. Experimental validation demonstrates that while standalone anomaly detection yields a low theft F1-score of 0.20, the proposed hybrid fusion achieves an overall accuracy of 93.7%. By calibrating decision thresholds via precision-recall analysis, the system attains a balanced theft precision of 0.55 and recall of 0.50, effectively mitigating the false positives inherent in single-model approaches. These results confirm that integrating topological grid awareness with temporal and supervised analytics provides a scalable, risk-based solution for proactive electricity theft detection and enhanced smart grid reliability.

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.

FinTexTS: Financial Text-Paired Time-Series Dataset via Semantic-Based and Multi-Level Pairing

The financial domain involves a variety of important time-series problems. Recently, time-series analysis methods that jointly leverage textual and numerical information have gained increasing attention. Accordingly, numerous efforts have been made to construct text-paired time-series datasets in the financial domain. However, financial markets are characterized by complex interdependencies, in which a company's stock price is influenced not only by company-specific events but also by events in other companies and broader macroeconomic factors. Existing approaches that pair text with financial time-series data based on simple keyword matching often fail to capture such complex relationships. To address this limitation, we propose a semantic-based and multi-level pairing framework. Specifically, we extract company-specific context for the target company from SEC filings and apply an embedding-based matching mechanism to retrieve semantically relevant news articles based on this context. Furthermore, we classify news articles into four levels (macro-level, sector-level, related company-level, and target-company level) using large language models (LLMs), enabling multi-level pairing of news articles with the target company. Applying this framework to publicly-available news datasets, we construct \textbf{FinTexTS}, a new large-scale text-paired stock price dataset. Experimental results on \textbf{FinTexTS} demonstrate the effectiveness of our semantic-based and multi-level pairing strategy in stock price forecasting. In addition to publicly-available news underlying \textbf{FinTexTS}, we show that applying our method to proprietary yet carefully curated news sources leads to higher-quality paired data and improved stock price forecasting performance.

Unpaired Cross-Domain Calibration of DMSP to VIIRS Nighttime Light Data Based on CUT Network

Defense Meteorological Satellite Program (DMSP-OLS) and Suomi National Polar-orbiting Partnership (SNPP-VIIRS) nighttime light (NTL) data are vital for monitoring urbanization, yet sensor incompatibilities hinder long-term analysis. This study proposes a cross-sensor calibration method using Contrastive Unpaired Translation (CUT) network to transform DMSP data into VIIRS-like format, correcting DMSP defects. The method employs multilayer patch-wise contrastive learning to maximize mutual information between corresponding patches, preserving content consistency while learning cross-domain similarity. Utilizing 2012-2013 overlapping data for training, the network processes 1992-2013 DMSP imagery to generate enhanced VIIRS-style raster data. Validation results demonstrate that generated VIIRS-like data exhibits high consistency with actual VIIRS observations (R-squared greater than 0.87) and socioeconomic indicators. This approach effectively resolves cross-sensor data fusion issues and calibrates DMSP defects, providing reliable attempt for extended NTL time-series.

Navigating Time's Possibilities: Plausible Counterfactual Explanations for Multivariate Time-Series Forecast through Genetic Algorithms

Counterfactual learning has become promising for understanding and modeling causality in complex and dynamic systems. This paper presents a novel method for counterfactual learning in the context of multivariate time series analysis and forecast. The primary objective is to uncover hidden causal relationships and identify potential interventions to achieve desired outcomes. The proposed methodology integrates genetic algorithms and rigorous causality tests to infer and validate counterfactual dependencies within temporal sequences. More specifically, we employ Granger causality to enhance the reliability of identified causal relationships, rigorously assessing their statistical significance. Then, genetic algorithms, in conjunction with quantile regression, are used to exploit these intricate causal relationships to project future scenarios. The synergy between genetic algorithms and causality tests ensures a thorough exploration of the temporal dynamics present in the data, revealing hidden dependencies and enabling the projection of outcomes under hypothetical interventions. We evaluate the performance of our algorithm on real-world data, showcasing its ability to handle complex causal relationships, revealing meaningful counterfactual insights, and allowing for the prediction of outcomes under hypothetical interventions.