Distributional conformal prediction
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We propose a robust method for constructing conditionally valid prediction intervals based on regression models for conditional distributions such as quantile and distribution regression. Our approach exploits the probability integral transform and relies on permuting estimated “ranks” instead of regression residuals. Unlike residuals, these ranks are independent of the covariates, which allows us to establish the conditional validity of the resulting prediction intervals under consistent estimation of the conditional distributions. We also establish theoretical performance guarantees under arbitrary model misspecification. The usefulness of the proposed method is illustrated based on two applications. First, we study the problem of predicting daily returns using realized volatility. Second, we consider a synthetic control setting where the goal is to predict a country's counterfactual GDP growth rate based on the contemporaneous GDP growth rates of other countries.
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