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

Area of Science:

• Time Series Analysis
• Statistical Forecasting
• Operations Research

Background:

• Hierarchical time series forecasting relies on reconciliation for coherence.
• Current methods like Minimum Trace (MinT) optimize variance but distort forecast shape.
• Variance-optimal coherence is insufficient for practical applications.

Purpose of the Study:

• To reframe forecast reconciliation as a multi-objective problem.
• To develop a shape-aware reconciler that preserves temporal structure.
• To introduce a novel framework, Shape-Preserving Minimum Trace (SP-MinT), for improved forecast reconciliation.

Main Methods:

• Formulated forecast reconciliation as a multi-objective optimization problem.
• Introduced domain-informed priors based on historical day-of-week profiles.
• Developed the Shape-Preserving Minimum Trace (SP-MinT) framework.

Main Results:

• SP-MinT significantly reduces Root Mean Squared Error (RMSE) by 31.94%.
• SP-MinT achieves a 43.16% reduction in Shape Error (Dynamic Time Warping).
• Outperformed the standard MinT-WLS benchmark in rolling cross-validation on electricity demand data.

Conclusions:

• SP-MinT offers superior forecast reconciliation by balancing statistical accuracy and morphological fidelity.
• The method provides hierarchically coherent forecasts that respect physical ramping constraints.
• SP-MinT enhances operational decision-making for grid operators through improved forecast reliability.