Forecast Combination and Reconciliation
Forecasts play a central role in decision-making across economics, business, energy, and policy. So far, two recurring challenges arise in practice. First, forecasts often need to satisfy logical or accounting constraints: for example, national GDP must equal the sum of its income, expenditure, and output measures; or total electricity demand must equal the sum of demand across regions and fuel types. Producing forecasts that are accurate and also coherent can be challenging. Second, forecasts may come from multiple sources: different models, experts, or institutions frequently produce competing forecasts, each capturing different aspects of the underlying system. How can we combine these multiple forecasts, while also satisfying the necessary constraints?
This talk introduces coherent forecast combination, a framework that addresses these two challenges simultaneously. It extends the well-established idea of forecast reconciliation by integrating it with the broader task of forecast combination. In doing so, it leverages the strengths of both approaches: forecast combination improves accuracy by pooling diverse sources of information, while reconciliation ensures that forecasts satisfy the required constraints or accounting identities. We consider different linear approaches. First, combination and reconciliation are solved together in a single optimization step, producing forecasts that are both accurate and coherent by design. Then, we present a sequential approach, where the two steps are performed one after the other: we can first combine forecasts for each individual variable and then reconcile them, or vice versa. Both strategies have practical advantages depending on the application, the data structure, and the availability of forecasts.
Finally, we show that coherent forecast combination delivers 15min forecasts of Italian energy load disaggregated by geographical bidding zones, that are both more accurate and aligned with the geographical constraints. This illustrates the value of this framework: making better use of the forecasts we already have, while ensuring results remain consistent and trustworthy. The open-source R package FoCo2 makes these approaches directly available for applied work.
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