Full conformal prediction offers finite-sample marginal coverage guarantees under exchangeability, but exact computation can be costly and its classical guarantees do not directly extend to non-stationary data streams. The authors compare four sequential conformal regression procedures against a weighted full-conformal benchmark, measuring empirical coverage, prediction interval width, and computational cost.
The procedures combine ordinary or forgetting-factor least squares with uniform or exponentially weighted empirical residual quantiles, or with online gradient-based quantile tracking. Experiments cover an i.i.d. control setting, two synthetic distribution-shift scenarios, and four real-world data streams.
The central finding is that adapting both the regression model and the conformal threshold substantially improves the coverage–width tradeoff under drift. The quantile-tracking procedure requires O(p^2) time and memory per observation, independent of stream length, although its coverage can deteriorate after abrupt changes. These results illustrate practical tradeoffs between predictor adaptation, uncertainty quantification, and computational resources.