An Alternative Proof of Minimum Trace Reconciliation

Sakai Ando and Futoshi Narita

No 2022/136, IMF Working Papers from International Monetary Fund

Abstract: Minimum trace reconciliation, developed by Wickramasuriya et. al. (2019), is an innovation in the literature of forecast reconciliation. The proof, however, is indirect and not easy to extend to more general situations. This paper provides an alternative proof based on the first-order condition in the space of non-square matrix and argues 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.

Keywords: Forecast Reconciliation; Minimum Trace Reconciliation; Hierarchical Time Series; IMF working papers; trace reconciliation; covariance matrix; choice matrix p; GDP forecasting; weight matrix; forecast error; lower bound function; lower bound minimization; n×m matrix (search for similar items in EconPapers)
Pages: 12
Date: 2022-07-08
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