2022-07-07-IMF-An_Alternative_Proof_of_Minimum_Trace_Reconciliation_12页_938kb

Alternative Proof of Minimum Trace Reconciliation
This paper provides an alternative and simpler proof for the minimum trace reconciliation method developed by Wickramasuriya et al. (2019). The original proof was indirect and difficult to extend to more general cases. By solving the first-order condition in the space of non-square matrices, the alternative proof is more direct and facilitates extensions to weighted trace reconciliation, as shown in Panagiotelis et al. (2021). The insight remains unified and pedagogical, demonstrating that the optimal reconciliation matrix minimizes trace under linear constraints without trade-offs between variables. This contributes to a clearer understanding of forecast reconciliation in hierarchical time series.