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 \\(\\rho \\) , and a higher-capacity fine stage scores only those candidates; in this screening regime ( \\(\\rho <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- \\(\\rho \\) 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\\pm 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 \\(\\rho =0.5\\) preserves the full-evaluation \\(F_1\\) (paired \\(\\Delta F_1=+0.001\\pm 0.004\\) , five seeds) while halving the fine-stage workload, and the same gate improves a Transformer fine detector (paired \\(\\Delta F_1=+0.112\\pm 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.