Forecasting under Changing Response Delays: Prediction and Memory When Relations Disappear

An upstream signal may remain useful when its response arrives later, but rising forecast error can also reflect a broken relation or increased noise. We study what a forecaster should predict and remember across these changes. A target-history model fitted while the relation is active can absorb the source effect it must later predict without. Evaluating the shared relation at a training-input reference improves cancellation prediction in two controlled mechanisms. We derive how the inactive prediction also changes effective delay refresh through posterior mass. Matching conditional delay weights preserves the cancellation benefit, while different return rules change its size in opposite directions. Remembering inactive delays helps old-delay recurrence and costs accuracy when a new delay returns. A fixed reference/adaptive configuration reduces noise error by 31.3% on new synthetic streams and 10.6% on semisynthetic streams driven by household measurements, relative to a fixed-scale joint tracker. It meets the synthetic criteria but fails the joint test because external delay and stable-window errors exceed their tolerances. A fixed refresh control is competitive. Changing the inactive target level reverses the reference's advantage; learning an offset mitigates this at a transient cost. These results identify a practical coupling: the forecast assigned to inactivity determines both immediate error and how much delay information survives for future use.