An Alternative Proof of Minimum Trace Reconciliation

Abstract

Minimum trace reconciliation, developed by Wickramasuriya et al., 2019, is an innovation in the literature on forecast reconciliation. The proof, however, has a gap, and the idea is not easy to extend to more general situations. This paper fills the gap by providing an alternative proof based on the first-order condition in the space of a non-square matrix and arguing that it is not only simpler but also can be extended to incorporate more general results on minimum weighted trace reconciliation in Panagiotelis et al., 2021. Thus, our alternative proof not only has pedagogical value but also connects the results in the literature from a unified perspective.