Forecasting with temporal hierarchies


George Athanasopoulos, Rob J Hyndman, Nikolaos Kourentzes, Fotios Petropoulos


13 May 2017

Publication details

European Journal of Operational Research, 262(1) 60–74



This paper introduces the concept of Temporal Hierarchies for time series forecasting. A temporal hierarchy can be constructed for any time series by means of non-overlapping temporal aggregation. Predictions constructed at all aggregation levels are combined with the proposed framework to result in temporally reconciled, accurate and robust forecasts. The implied combination mitigates modelling uncertainty, while the reconciled nature of the forecasts results in a unified prediction that supports aligned decisions at different planning horizons: from short-term operational up to long-term strategic planning. The proposed methodology is independent of forecasting models. It can embed high level managerial forecasts that incorporate complex and unstructured information with lower level statistical forecasts. Our results show that forecasting with temporal hierarchies increases accuracy over conventional forecasting, particularly under increased modelling uncertainty. We discuss organisational implications of the temporally reconciled forecasts using a case study of Accident & Emergency departments.

Keywords: Hierarchical forecasting, temporal aggregation, reconciliation, forecast combination

The thief package implements the methods in this paper.