Conformalized Quantile Regression for Time Series Probabilistic Forecasting

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Uncertainty in predictions is important for decision-makers to understand the range of potential outcomes and associated risks. By quantifying uncertainty, an organization can make more informed decisions and allocate resources effectively. On prediction uncertainty, we have learned the Quantile Regression (QR) technique and the Conformal Prediction (CP) technique in the previous chapters “Quantile Regression for Time Series Probabilistic Forecasting” and “Conformal Predictions for Time Series Probabilistic Forecasting”. This chapter will explain another important technique — the Conformalized Quantile Regression (CQR). As its name suggests, it combines Quantile Regression (QR) and Conformal Prediction (CP), making both complement each other.

Let’s think of QR first. We like QR because it estimates the conditional quantiles of the target variable such as the median or the 90th percentile, rather than the conditional mean. It can handle heteroscedasticity well by estimating the…