A general framework for multi-step ahead adaptive conformal heteroscedastic time series forecasting

The exponential growth of machine learning (ML) has prompted a great deal of interest in quantifying the uncertainty of each prediction for a user-defined level of confidence. Reliable uncertainty quantification is crucial and is a step towards increased trust in AI results. It becomes especially important in high-stakes decision-making, where the true output must be within the confidence set with high probability. Conformal prediction (CP) is a distribution-free uncertainty quantification framework that works for any black-box model and yields prediction intervals (PIs) that are valid under the mild assumption of exchangeability. CP-type methods are gaining popularity due to being easy to implement and computationally cheap; however, the exchangeability assumption immediately excludes time series forecasting. Although recent papers tackle covariate shift, this is not enough for the general time series forecasting problem of producing H-step ahead valid PIs. To attain such a goal, we propose a new method called AEnbMIMOCQR (Adaptive ensemble batch multiinput multi-output conformalized quantile regression), which produces asymptotic valid PIs and is appropriate for heteroscedastic time series. We compare the proposed method against state-of-the-art competitive methods in the NN5 forecasting competition dataset. All the code and data to reproduce the experiments are made available