Reconciliation of aggregated and disaggregated time series forecasts in nonparametric forecasting problems

In many applications, there are the problems of forecasting a lot of time series with hierarchical structure. It is needed to reconcile forecasts across the hierarchy. In this paper, a new algorithm of reconciliation of hierarchical time series forecasts is proposed. This algorithm is based on solving the optimization problem with constraints. The proposed algorithm allows to reconcile the forecasts with nonplanar hierarchical structure and to take into account physical constraints of forecasted values such as nonnegativeness or maximal value. The algorithm performance is illustrated by the railroad stations occupancy data in the Omsk region. The quality of forecasts is compared with the quality of forecasts made by the optimal algorithm of reconciliation. Also, the algorithm performance is demonstrated for the nonplanar hierarchical structure of time series.