Forecast Reconciliation: A Review

Collections of time series that are formed via aggregation are prevalent in many fields. These are commonly referred to as hierarchical time series and may be constructed cross-sectionally across different variables, temporally by aggregating a single series at different frequencies, or may even be generalised beyond aggregation as time series that respect linear constraints. When forecasting such time series, a desirable condition is for forecasts to be coherent, that is to respect the constraints. The past decades have seen substantial growth in this field with the development of reconciliation methods that not only ensure coherent forecasts but can also improve forecast accuracy. This paper serves as both an encyclopaedic review of forecast reconciliation and an entry point for researchers and practitioners dealing with hierarchical time series. The scope of the article includes perspectives on forecast reconciliation from machine learning, Bayesian statistics and probabilistic forecasting as well as applications in economics, energy, tourism, retail demand and demography.