CoLDM: Component‑Wise Lead–Lag‑Aware Dependency Modeling for Multivariate Time-Series Anomaly Detection in IoT

In Internet of Things (IoT) and industrial IoT (IIoT) systems, interconnected sensors continuously generate nonstationary multivariate time series (MTS), where inter-variable dependencies vary across operating regimes. Consequently, anomalies may manifest not only as point-wise deviations but also as abnormal changes in dependency patterns, especially lead–lag interactions induced by propagation delays and system responses. Reliably detecting such anomalies requires accurately modeling time-varying inter-variable dependencies. However, existing methods mainly focus on instantaneous correlations or lagagnostic dependency learning in the feature space, thereby over-looking lead–lag-aware dependency structures which are crucial for detecting anomalies in nonstationary environments. We propose CoLDM, an unsupervised reconstruction-based framework that learns lead-lag-aware inter-variable dependency representations for MTS anomaly detection. CoLDM first extracts statistical lead–lag cues and converts them into a soft structural prior, which is injected via Structural Preference Modulation to guide dependency learning. Moreover, CoLDM adopts a componentwise dual-branch architecture to capture complementary lead–lag dependency information, and introduces a component-adaptive latent fusion module that adaptively integrates the two representations across regimes, reducing redundant overlap and improving robustness. Experiments on real-world benchmarks demonstrate that CoLDM generalizes well and remains robust under nonstationary regimes.