Probabilistic Reconciliation of Count Time Series

For example, the total sales of a product in a country can be divided into regions and then into sub-regions. Forecasts of hierarchical time series should be coherent; for instance, the sum of the forecasts of the different regions should be equal to the forecast for the entire country. Forecasts are incoherent if they do not satisfy such constraints. Reconciliation methods [13, 31] compute coherent forecasts by combining the base forecasts generated independently for each time series, possibly incorporating non-negativity constraints [32]. Reconciled forecasts are generally more accurate than the base forecasts; indeed, forecast reconciliation is related to forecast combination [9, 6]. A special case of reconciliation is constituted by temporal hierarchies [1], which reconcile base forecasts computed for the same variable at different frequencies (e.g., monthly, quarterly and yearly); they generally improve the forecasts [19] of smooth and intermittent time series. As for probabilistic reconciliation, [25] proposed a seminal framework which interprets reconciliation as a projection.