Modular and Adaptive Conformal Prediction for Sequential Models via Residual Decomposition

Conformal prediction offers finite-sample coverage guarantees under minimal assumptions. However, existing methods treat the entire modeling process as a black box, overlooking opportunities to exploit modular structure. We introduce a conformal prediction framework for two-stage sequential models, where an upstream predictor generates intermediate representations for a downstream model. By decomposing the overall prediction residual into stage-specific components, our method enables practitioners to attribute uncertainty to specific pipeline stages. We develop a risk-controlled parameter selection procedure using family-wise error rate (FWER) control to calibrate stage-wise scaling parameters, and propose an adaptive extension for non-stationary settings that preserves long-run coverage guarantees. Experiments on synthetic distribution shifts, as well as real-world supply chain and stock market data, demonstrate that our approach maintains coverage under conditions that degrade standard conformal methods, while providing interpretable stage-wise uncertainty attribution. This framework offers diagnostic advantages and robust coverage that standard conformal methods lack.