Forecast Privately, Correct Minimally:Bounded Relational Interventions for Multivariate Time Series

Cross-variable information can improve multivariate forecasting, yet an unrestricted mixer can also replace reliable channel-private dynamics and propagate local faults to healthy channels. We ask a narrower question: how much relational intervention is sufficient? We introduce the Minimum-Intervention Relational Forecaster (MIRF), which first produces a complete channel-private temporal representation and then applies one identity-start residual correction. A C-r-C factorization limits the correction to r channel directions, while spectral caps and a bounded scalar gain limit its magnitude. This design uses one ordinary MAE objective and no auxiliary routing or decomposition losses. Under a fixed look-back of 96 and four forecast horizons, MIRF ranks first in 12 of 16 dataset-average MSE/MAE cells across eight benchmarks and a compact recent baseline set, including two 2026 methods. Controlled relation misalignment and sensor-outage tests show why the constraint matters. On Traffic with 50% channel outage, the selected bounded correction incurs 14.11% untouched-channel MSE spillover, compared with 41.90% for an unbounded low-rank correction and 111.72% for an unbounded dense correction. At 862 channels, rank four uses 207.8 fewer relational parameters and runs 37.7 faster at inference than the matched dense correction. These results support a minimum-intervention principle: relational structure is most useful as a controlled amendment to a private forecast, rather than as its unrestricted replacement.