When Does History Transfer? Conditional Historical-Error Reuse under Temporal Regime Shift

Historical forecast errors can improve predictions under distribution shift, but their value depends on which history is retrieved, whose errors are reused, and how strongly the resulting correction is trusted. We study these decisions through a decomposable historical-error memory for multivariate forecasting. On 31 global equity indices, joint-market-state retrieval reduces equal-market QLIKE by 2.78% relative to matched local-state retrieval, showing that other series help identify which history is relevant even when only the target series' own errors are reused. A two-parameter own-error correction improves HARX by 2.77% and nearly matches a source-specific graph. When access to own historical errors is disabled at query time, source-specific fallback improves uniform-source fallback by 0.75%. Past-loss adaptive trust further lowers QLIKE, although its advantage over the strongest fixed equal-weight mixture is statistically unresolved. The results suggest a conditional transfer principle: retrieve history using the joint system state, reuse own errors by default, borrow cross-series errors when own memory is unavailable, and adapt correction strength only when it improves over strong fixed baselines.