Coherent forecast combination for linearly constrained multiple time series

Forecasting linearly constrained multiple time series, as those arising in National Accounts, energy systems and supply chain planning, requires that the forecasts of all variables jointly satisfy the underlying accounting or resource-balance identities. When several experts provide forecasts for some or all of the variables, classical forecast combination operates on each variable and ignores the linear constraints, while forecast reconciliation enforces such constraints by using a single forecast per variable. To bridge this gap, we develop an original coherent forecast combination framework, in which the joint problem of combination across experts and coherence across variables is formulated as a linearly constrained optimization problem. Closed-form expressions are derived for the coherent combined forecast and its error covariance matrix, and the statistical properties of the resulting estimators are discussed. A Monte Carlo experiment and a forecasting application to an Australian daily electricity generation dataset confirm that the proposed approach significantly improves forecast accuracy with respect to standard forecast combination and reconciliation alternatives.