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 .
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 many 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 arbitrary heteroskedasticity. We establish the conditional validity under consistent estimation and also provide theoretical performance guarantees under model misspecification, overfitting, and with time series data .
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regression
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can be applied to many important prediction problems including cross-sectional prediction, k-step-ahead forecasts, synthetic controls and counterfactual prediction, and individual treatment effects prediction. Our method
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``ranks'' instead of regression residuals. Unlike residuals, these
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. Unlike regression residuals, ranks
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covariates, which allows us to
predictors, allowing us to construct conditionally valid prediction intervals under arbitrary heteroskedasticity. We
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of the resulting prediction intervals
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of the conditional distributions. We also establish
and also provide
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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
model misspecification, overfitting, and with time series data