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 since nowadays ML is increasingly being used in high-stakes settings. Reliable ML via prediction intervals (PIs) that take into account jointly the epistemic and aleatory uncertainty is therefore imperative and is a step towards increased trust in model forecasts. Conformal prediction (CP) is a lightweight distribution-free uncertainty quantification framework that works for any black-box model, yielding 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 from the stage. Although recent papers tackle distribution shift and asymptotic versions of CP, 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 multi-input multi-output conformalized quantile regression), which produces valid PIs asymptotically 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.