Hierarchical coarse-to-fine anomaly detection for high-dimensional time series

High-dimensional time-series anomaly detection must balance detection quality against computational cost under evaluation protocols that respect time order. We present a hierarchical coarse-to-fine framework: a low-capacity coarse stage screens the record into a candidate set of retained fraction \(ρ \) , and a higher-capacity fine stage scores only those candidates; in this screening regime ( \(ρ <1\) ) the gate directly shapes final predictions and fine-stage workload. Evaluation on a redesigned synthetic benchmark with moderate contamination ( \(21.4%\) of time points) is chronological: no future information is used in model fitting, configuration selection, or threshold calibration; the primary top- \(ρ \) analysis is retrospective and batch-based; a causal, validation-calibrated gate is evaluated separately. The detector best matched to this near-linear–Gaussian benchmark—a lightweight PCA reconstruction—attains the best held-out \(F_1\) ( \(0.929± 0.019\) over five seeds) at a fraction of the deep models’ cost. Screening by an eight-component PCA coarse stage at a pre-specified retained fraction \(ρ =0.5\) preserves the full-evaluation \(F_1\) (paired \(Δ F_1=+0.001± 0.004\) , five seeds) while halving the fine-stage workload, and the same gate improves a Transformer fine detector (paired \(Δ F_1=+0.112± 0.031\) ) while roughly halving its fine-stage inference time. These results reflect detector–benchmark match on controlled synthetic data, not general superiority of linear methods.