Aug 2026· Environmetrics· Vol 37· 1 citation· 44 references
TL;DR
NLDNAR‐CP is proposed, a novel change point detection method within a node‐specific NAR framework that accommodates heterogeneous temporal dependencies across variables and efficiently detects multiple structural breaks while preserving scalability to high‐dimensional networks.
Abstract
Understanding temporal dynamics in complex systems often requires identifying abrupt structural changes, known as change points in multivariate time series. Traditional vector autoregressive (VAR) models have been widely used for modeling dependencies across time, yet their parameter space grows quadratically with the number of variables, leading to computational and estimation challenges in high‐dimensional settings. The recently proposed network autoregressive (NAR) modeling framework offers a computationally efficient alternative by reducing parameter complexity through a network‐based representation. However, existing NAR models either assume homogeneous temporal behavior across all nodes, overlooking node‐specific dynamics that frequently arise in environmental and socio‐economic systems, or do not allow for structural breaks. In this work, we propose NLDNAR‐CP, a novel change point detection method within a node‐specific NAR framework that accommodates heterogeneous temporal dependencies across variables. The proposed approach efficiently detects multiple structural breaks while preserving scalability to high‐dimensional networks. We demonstrate the method's superior empirical performance through extensive simulations and a real‐world environmental application.
A novel theoretical model, namely the multiway autoregressive (MARS) model, which characterizes multiple evolutionary paths by capturing dependencies within and across two core factors underlying diverse evolutionary mechanisms is proposed, which develops a general DGNN framework, a multiway autoregressive network (MAN).
Ping He, Xiao-hua Xu· IEEE Transactions on Neural...· 0 citations
Effectively modeling the complex and evolving dependencies among multiple variables is a key challenge in multivariate time series anomaly detection (MTSAD). Existing methods typically model channel dependencies in discrete time steps, either window-wise or point-wise. However, they face a granularity dilemma: window-wise approaches are too coarse to capture transient local changes, whereas fine-grained methods lack constraints on dependency continuity, making them susceptible to high-frequency noise and leading to dependency oscillation. Furthermore, since self-channel correlations typically dominate cross-channel signals, existing methods are biased towards self-dependencies, often overlooking subtle cross-channel deviations that indicate anomalies. In this paper, we propose LatentFlow, a novel framework that treats channel dependency evolution as a latent continuous dynamic process. Specifically, we model the evolution of channel dependencies using an Ornstein-Uhlenbeck (O-U) process. This introduces a mean-reverting property and structural inertia, allowing the model to capture smooth dependency shifts while maintaining robustness against structural noise. Additionally, we introduce a Dependency Decoupling Strategy to explicitly separate and rebalance self- and cross-channel patterns. Extensive experiments on multiple real-world datasets demonstrate that LatentFlow achieves state-of-the-art performance, validating the effectiveness of modeling the continuous dynamics of dependency evolution.
Lijun Sun, Shuai Zhang, Xin Xue et al.· Proceedings of the 32nd ACM...· 0 citations
High-dimensional functional panels consist of temporally ordered curves observed across many subjects and naturally exhibit heterogeneous structural changes. Under sparse subject-level break signals or opposite-signed shifts, traditional mean-aggregated CUSUM procedures may suffer noticeable power loss due to signal attenuation or cancellation induced by cross-sectional averaging. We propose a novel Energy--PE statistic, which combines subject-wise squared CUSUM energy aggregation with a generalized power-enhancement component. The energy aggregation preserves subject-level evidence under sign-heterogeneous changes, while the power-enhancement component improves sensitivity to sparse weak break signals. Under regularity conditions, we establish the asymptotic behavior of the proposed statistic. We further incorporate a latent group structure and an information-criterion-based clustering algorithm to estimate the unknown group number and membership for heterogeneous break points. Numerical studies and an intraday stock application demonstrate that Energy--PE controls size, improves power under sparse and sign-heterogeneous alternatives, and yields interpretable post-test summaries.
Xu-Fei Tang, Dan Zhuang, Hou-Lin Zhou· 0 citations
Time series forecasting is fundamental to intelligent decision-making systems, enabling proactive planning and resource optimization across diverse application domains. However, the inherent complexity of real-world time series—including multi-scale temporal patterns, heterogeneous variable dependencies, and dynamic non-stationarity—poses significant challenges for existing forecasting models. Current approaches often suffer from high-frequency information attenuation in frequency-domain modeling, inadequate characterization of scale heterogeneity across variables, and limited capability to capture time-varying dynamics. To address these challenges, this paper introduces AdaDyTS, a unified knowledge-driven forecasting framework that synergistically integrates three complementary mechanisms: multi-scale frequency-domain interpolation decoupling via the Cascaded Spectral Residual Extractor (CSRE), dynamic morphological perception via the Dynamic Morphological Perception Unit (DMP-U), and time-variant state-space inference via the Time-Variant State-Space Module (TV-SS). CSRE separates low-frequency trends from high-frequency residuals through coarse-to-fine layer-wise self-reconstruction, preserving transient information that static filters typically attenuate. DMP-U employs deformable convolution guided by multi-expert attention to adaptively adjust receptive fields, enabling fine-grained modeling of local fluctuations and nonlinear distortions. TV-SS relaxes the conventional time-invariant parameter assumption, dynamically modulating state transition parameters to capture both short-term variations and long-term dependencies. Under a unified evaluation protocol across 13 benchmark datasets, AdaDyTS achieves average improvements of 4.35\% in MSE and 4.31\% in MAE over the AMD backbone, consistently outperforming state-of-the-art methods across long-horizon forecasting scenarios. The proposed framework demonstrates the effectiveness of integrating domain-specific knowledge—including spectral analysis, morphological feature extraction, and dynamic system modeling—within a unified deep learning architecture for enhanced predictive performance.
Jin-Lai Zhang· Poster Volume 0008 The 2026...· 0 citations
We develop a framework for simultaneous change-point inference of high-dimensional functional time series. The observations are modeled as temporally dependent vectors whose coordinates take values in possibly different separable Hilbert spaces, thereby covering a broad class of functional data. Heterogeneous mean changes may occur at coordinate-specific locations, and the contemporaneous dependence across coordinates is left unrestricted. Our procedure is based on coordinatewise cumulative-sum statistics and a residual block multiplier bootstrap that provides a common critical value for the global test and all coordinatewise decisions. We establish a nonasymptotic Gaussian approximation, quantitative nonasymptotic bounds for strong family-wise error control under arbitrary mixtures of changed and unchanged coordinates, covariance-adaptive detection guarantees, and simultaneous high-probability bounds for change-point localization. The bounds accommodate high-dimensional regimes in which the number of functional coordinates grows exponentially in a power of the sample size. We investigate finite-sample performance in simulations and illustrate the method using river discharge curves and high-frequency financial log returns.
Multivariate time series anomaly detection (MTSAD) plays a critical role in monitoring complex systems, where anomalies often arise from both abnormal temporal dynamics and irregular inter-variable interactions. Despite extensive research, existing methods vary widely in how temporal and spatial dependencies are modeled, making it difficult to systematically understand their design principles and limitations. In this survey, we review MTSAD methods from a unified spatial–temporal representation learning perspective. We analyze how temporal dependencies and inter-channel relationships are captured, and organize existing approaches into a coherent taxonomy based on implicit and explicit guidance mechanisms. Temporal modeling strategies are analyzed in terms of implicit dependency learning and explicitly guided temporal priors, while spatial modeling approaches are categorized into implicit and explicit guidance mechanisms, depending on whether inter-variable relationships are learned in a purely data-driven manner or guided by explicitly designed structural priors. Through this structured analysis, we highlight key design considerations related to modeling flexibility, robustness, and interpretability. This survey aims to clarify the evolving landscape of spatial–temporal anomaly detection and to provide insights for developing more reliable, interpretable, and scalable MTSAD frameworks.
Yin-Song Xu, Yu-Huan Liu, Yu-Long Ding et al.· 2026 International Symposium...· 0 citations
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