GLTF-FEDformer: an adaptive time-frequency fusion method for multivariate time series anomaly detection enhanced by prediction error embedding

Abstract Multivariate time series are widespread in scenarios such as industrial IoT, smart manufacturing, energy systems, and medical monitoring. Their anomalous behaviors often involve complex patterns like long-range dependency changes, local dynamic shifts, transient spectral perturbations, and variable-association mismatches. Existing reconstruction-based and attention-based methods can learn the overall evolution of normal sequences but still lack fine-grained characterization of local time-frequency changes; moreover, relying solely on point-wise prediction errors for anomaly scoring struggles to fully reflect structural shifts in the error distribution. To address these issues, this paper proposes GLTF-FEDformer, a multivariate time series anomaly detection method that jointly models global and local time-frequency features. The method learns temporal dependencies, trend changes, and periodic candidate patterns from long-window contexts via a global temporal representation module, and enhances the modeling of temporal evolution through a continuous dynamic refinement mechanism. It also builds a lightweight local time-frequency feature extraction module that uses short-time Fourier transform, 2D convolutions, spectral gating, and inverse transforms to enhance the perception of local morphological changes, spectral perturbations, and time-frequency coupled features within local windows. A gated fusion mechanism performs data-dependent integration of global temporal information and local time-frequency information to obtain more discriminative prediction representations. Additionally, we design an anomaly scoring strategy based on a prediction-error-embedded profile, mapping prediction residuals into an embedding space and measuring structural deviations of test prediction-error embeddings from the normal error profile through variable-level standardized distances. The profile score is further combined with point-wise prediction errors to form anomaly responses with temporal localization ability. This strategy not only uses amplitude information of prediction errors but also captures structural shifts of the error distribution relative to normal patterns, thereby improving detection robustness in complex anomaly scenarios. Experimental results show the proposed method effectively enhances multivariate time series anomaly recognition and demonstrates strong detection performance and stability across various public datasets.