Matched Endpoints, Different Futures: Forecasting under Order-Dependent Non-Stationarity

Forecasting models can adapt to distribution shift and encode long histories, but these capabilities do not isolate whether temporal order remains predictive once the observable endpoint and the experienced transformations are fixed. We formalize this phenomenon as order-dependent predictive non-stationarity (ODN): matched-endpoint histories containing the same transformation instances in different orders induce different conditional futures. Under squared loss and balanced paired orders, collapsing a reversed-order pair incurs minimum excess risk equal to one quarter of the per-target squared separation between its conditional means. We introduce ORBIT (Ordered Residual Bias for Interacting Transitions), a compact forecasting adapter that converts local predictive changes into bounded low-rank corrections and composes them in temporal order. We analyze when this interaction separates reversed paths and how approximation error propagates through the composition. On the primary context-held-out $AB\to BA$ benchmark, ORBIT reduces unseen-order NMSE from $.158$ for Mamba to $.124$, a 21.5% reduction under matched training budgets and similar reported parameter scales. Removing or perturbing ordered composition increases paired error. An independent rotation diagnostic shows larger gain point estimates across increasing future-gap bins, and a no-auxiliary-loss variant retains a positive paired gain over Mamba. Across five semi-synthetic datasets, unseen-order error decreases by $12.25\%$. Together, these results support ordered composition as a useful inductive bias for forecasting under path-dependent shift.