Title: Provably Calibrated Regression Under Distribution Drift. Abstract: Accurate uncertainty quantification is a key building block of trustworthy machine learning systems. Uncertainty is typically represented by probability distributions over the possible outcomes, and these probabilities should be calibrated, \textit{e.g}. the 90\% credible interval should contain the true outcome 90\% of the times. In the online prediction setup, existing conformal methods can provably achieve calibration assuming no distribution shift; however, the assumption is difficult to verify, and unlikely to hold in many applications such as time series prediction. Inspired by control theory, we propose a prediction algorithm that guarantees calibration even under distribution shift, and achieves strong performance on metrics such as sharpness and proper scores. We compare our method with baselines on 19 time-series and regression datasets, and our method achieves approximately 2x reduction in calibration error, comparable sharpness, and improved downstream decision utility. 