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

While considerable effort has been dedicated to identifying the most effective approaches, with the widely recognized M forecasting competition, initiated in 1982 (Makridakis et al., 1982), serving as a arena for these breakthroughs, quantifying the uncertainty of such predictions has received diminished attention. Indeed, the inclusion of prediction intervals (PIs) began to be considered in forecasting competitions only from the M4 competition (Makridakis et al., 2020) onward. Another example of this discrepancy was observed in the M5 forecasting competitions. The M5 "Accuracy" competition (Makridakis et al., 2022a), which centered on optimizing point predictions, garnered significant interest and participation, with a staggering 7, 092 participants 2 vying for top honors. In stark contrast, the M5 "Uncertainty" competition (Makridakis et al., 2022b), which aimed to assess the quality of estimated conditional quantiles, drew considerably less attention, involving only 1, 137 participants despite offering the same prize incentives.