Uncertainty quantification in RoME

Background: Forecast reconciliation methods, including the proposed RoME, typically focus on producing accurate point forecasts that satisfy aggregation constraints. However, characterizing the predictive uncertainty associated with these reconciled forecasts is also a critical aspect of time series analysis.

Question / Future Work: Developing interval and probabilistic forecasts that quantify the uncertainty of reconciled results within the RoME framework is an important area for future work. While the approximate covariance matrix of reconciled forecast errors at each iteration offers a potential avenue for deriving such uncertainty measures, a rigorous theoretical justification for this integration remains to be established.