Forecast reconciliation: A geometric view with new insights on bias correction

A geometric interpretation is developed for so-called reconciliation methodologies used to forecast time series that adhere known linear constraints. In particular, a general framework established nests many existing popular methods within the class of projections. This facilitates derivation novel theoretical results. First, via projection guaranteed improve accuracy with respect loss functions based on generalised distance metric. Second, Minimum Trace (MinT) method minimises expected this same functions. Third, provides new proof using projections results in unbiased forecasts, provided initial base forecasts are also unbiased. Approaches dealing biased proposed. An extensive empirical study Australian tourism flows demonstrates paper and shows bias correction prior outperforms alternatives only bias-correct or reconcile forecasts.