An Alternative Proof of Minimum Trace Reconciliation

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 be extended to more general situations. This paper fills the gap by providing an alternative proof based on the first-order condition in the space of 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