Further developments in regression-based cross-temporal forecast reconciliation
Forecast reconciliation is a post-forecasting approach to ensure the coherence of forecasts across a variety of constraints (usually linear, not just simple aggregation). It harmonizes individual predictions to meet predefined relationships, leading to a consistent and comprehensive picture. This can include ensuring power generation for different photovoltaic plants sum up to the Independent System Operator (ISO), or guaranteeing some property (e.g. non negativity). By incorporating these constraints, reconciliation can also improve forecast accuracy by leveraging the individual strengths. In this talk, we address some open-issues related to the relationships between sequential, iterative, and optimal combination cross-temporal forecast reconciliation. We discuss the conditions under which a sequential (either first-cross-sectional-then-temporal, or first-temporal-then-cross-sectional) approach is equivalent to a fully (i.e., cross-temporally) coherent iterative heuristic. We also show that, for specific patterns of the error covariance matrix of the regression model on which the optimal combination approach grounds, iterative reconciliation “converges” to the optimal combination solution. The reduction of the computing effort is evaluated in an experiment on the SPDIS, an hourly photovoltaic power generation dataset, using the R package FoReco.