Conditional Quantile Adjusted Conformal Prediction for Time Series

Conformal prediction is challenging for time series with time-varying conditional distributions. Existing sequential conformal methods can yield volatile, non-nested prediction intervals due to noisy tail conditional quantile estimation and quantile crossing issue. To overcome these challenges, we construct prediction intervals for time series via a novel method called Conditional Quantile Adjusted Conformal Prediction (CQACP), which stabilizes sequential conformal calibration by modeling the conditional quantile curve of nonconformity score. At each time step, CQACP evaluates a base conditional quantile learner on a grid of quantile levels and fits a Cornish--Fisher approximation parameterized by conditional moments of nonconformity score with monotonicity constraints. Asymptotically, we prove the conditional validity of the prediction interval under serial dependence and show improved conditional quantile estimation accuracy. Experiments on multiple real-world datasets demonstrate that CQACP maintains accurate coverage and produces smooth, narrow, and nested prediction intervals across different significance levels and prediction models.

Many real-world forecasting problems, such as financial risk monitoring, energy demand prediction, and exchange-rate forecasting, require not only a point prediction but also a reliable range of possible future values. Existing uncertainty-quantification methods for time series can produce prediction intervals that behave inconsistently across confidence levels. This paper proposes a method called Conditional Quantile Adjusted Conformal Prediction, which stabilizes these intervals by learning the shape of the uncertainty curve across multiple confidence levels. The method produces prediction intervals that are accurate, smoother, and properly nested, meaning that higher-confidence intervals contain lower-confidence ones. Experiments on several real-world time-series datasets show that the proposed method provides reliable uncertainty estimates while keeping the intervals narrow and practically useful.