Distributional conformal prediction

We propose a robust method for constructing conditionally valid prediction intervals based on models for conditional distributions such as quantile and distribution regression. Our approach can be applied to important prediction problems, including cross-sectional prediction, k-step-ahead forecasts, synthetic controls and counterfactual prediction, and individual treatment effects prediction. Our method exploits the probability integral transform and relies on permuting estimated ranks. Unlike regression residuals, ranks are independent of the predictors, allowing us to construct conditionally valid prediction intervals under heteroskedasticity. We establish approximate conditional validity under consistent estimation and provide approximate unconditional validity under model misspecification, under overfitting, and with time series data. We also propose a simple shape adjustment of our baseline method that yields optimal prediction intervals.

Automated summary

Our method offers a robust approach to constructing valid prediction intervals based on conditional distribution models, such as quantile and distribution regression. By leveraging the probability integral transform and permuting estimated ranks, we can achieve conditionally valid prediction intervals even under heteroskedasticity. Additionally, we provide approximate conditional validity under consistent estimation and propose a shape adjustment to optimize prediction intervals.