A note on forecast reconciliation

Forecast reconciliation is a highly effective methodology for improving the predictive accuracy of multiple time series that are subject to linear constraints. This note provides an alternative derivation of the optimal reconciled predictor, based on linear projection arguments, under a set of minimal assumptions on the nature of the reconciliation error. Our result clarifies the relationship between the latter and the preliminary prediction error and encompasses well-known partial reconciliation problems, such as optimal linear disaggregation.