Relaxing stationarity for time-series model averaging

Determine whether the strict stationarity and ergodicity assumptions used to establish asymptotic coverage for Algorithm 1 can be relaxed to allow restricted distributional changes in the joint process of predictors and outcomes, and develop and validate the necessary algorithmic modifications that preserve coverage for conformal prediction intervals in the time-series model averaging setting.

Background

The paper’s asymptotic validity result for time-series data relies on strict stationarity and ergodicity of the joint process (x_t, y_t). The authors note that this assumption is generally necessary for covering random outcomes with specified probabilities, but suggest that it might be possible to relax it under controlled forms of distributional drift.

They reference weighted conformal inference approaches that handle covariate shift and distributional drift, and explicitly state that adapting such methods to the model averaging context remains to be done. This frames a concrete open direction: formalizing conditions under which coverage can be maintained when distributions change over time and specifying algorithmic adjustments for model averaging.

References

Meanwhile, we conjecture that this assumption may be relaxed to allow for restricted distributional changes with appropriate modifications to the algorithm. We leave the adaptation of such methods to model averaging for further work.

— Prediction Intervals for Model Averaging  (2510.16224 - Qu et al., 17 Oct 2025) in Section 4.2 (Asymptotic validity under stationarity)

The conformal guarantee is calibrated within the historical regime. A band can be narrow and wrong if the regime shifts, and the system's defense against that lived in the structural-break guard, which this run reports as not operative. That exclusion is therefore now open rather than delegated.

— ACT, WAIT, or EXPERIMENT: A Causal Governance Framework for Retail Price Optimization Under Abstentions  (2609.10615 - Cadahia, 8 Sep 2026) in Section 5.6, “Declared limitations,” item 6; Appendix, Section “Declared open gaps” under Governance Thresholds and Correspondence with the Implementation