Forecast combination for temporal hierarchies
Forecasts for a time series may be produced at multiple temporal frequencies, resulting from linear relationships across temporal levels. Temporal reconciliation methods exploit these relationships to produce forecasts that are consistent across temporal levels, typically relying on a single base forecast for each series at each temporal frequency.
In many real-world applications, several competing forecasts are available for the same target variable, generated by alternative models that differ in complexity, specification, and economic content. Forecast combination is widely recognized as an effective strategy for improving accuracy; however, its integration with temporal reconciliation has received limited attention.
A framework that jointly performs forecast combination and temporal reconciliation is proposed, allowing multiple forecasts to be combined while enforcing the linear relationships linking temporal levels. The resulting forecasts are coherent across temporal levels while exploiting the information contained in multiple predictive models. The methodology builds on recent developments in coherent forecast combination for linearly constrained multiple time series, and extends them to temporal reconciliation.