Shape-preserving minimum trace (SP-MinT): a regularized forecast reconciliation method for hierarchical time series

Forecast reconciliation has become the standard for ensuring coherence in hierarchical time series. However, state-of-the-art methods like Minimum Trace (MinT) prioritize the minimization of error variance, often at the expense of distorting the temporal morphology of the forecast. This paper reframes forecast reconciliation as a multi-objective problem, showing that variance-optimal coherence is insufficient for operational decision-making, and proposing a shape-aware reconciler that explicitly encodes temporal structure. We introduce Shape-Preserving Minimum Trace (SP-MinT), a novel framework that regularizes the optimization process with domain-informed priors constructed from historical day-of-week profiles. We validate the method using a rigorous rolling cross-validation on real-world electricity demand data from Victoria, Australia. The results demonstrate that SP-MinT outperforms the standard MinT-WLS benchmark by reducing the Root Mean Squared Error (RMSE) by 31.94% and the Shape Error (Dynamic Time Warping) by 43.16%. By bridging the gap between statistical optimality and morphological fidelity, SP-MinT offers grid operators hierarchically coherent forecasts that respect physical ramping constraints.