PROJECTION-CALIBRATED RESIDUAL ADAPTER FOR FROZEN TIME-SERIES FORECASTERS

Time-series forecasters can leave systematic prediction errors that admit correction without modifying the frozen backbone. Effective correction requires estimating both the temporal shape of the residual and the strength with which it should be corrected. We introduce the Projection-Calibrated Residual Adapter (PCRA), which supervises these factors separately. PCRA learns orthogonal temporal directions to represent complementary error patterns and uses analytical projection targets to supervise their signed strengths. For a fixed unit direction, the residual projection minimizes reconstruction error; orthogonality extends this result to decoupled coefficient targets. Implemented with lightweight MLPs, PCRA also supports test-time adaptation by updating the entire strength gate using fully observed historical outcomes. A conditional risk analysis characterizes when predictable residual energy captured by the directions exceeds coefficient prediction error. Static experiments on six supervised forecasters show a mean MSE reduction of 4.52% across five benchmarks; additional results demonstrate applicability to four frozen foundation models.