An Alternative Proof of Minimum Trace Reconciliation

An Alternative Proof of Minimum Trace Reconciliation
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Volume/Issue: Volume 2022 Issue 136
Publication date: July 2022
ISBN: 9798400216312
$20.00
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Topics covered in this book

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Economics- Macroeconomics , Economics / General , 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

Summary

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.