An Alternative Proof of Minimum Trace Reconciliation

July 8, 2022

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Format: Chicago

Sakai Ando, and Futoshi Narita. An Alternative Proof of Minimum Trace Reconciliation, (USA: International Monetary Fund, 2022) accessed December 25, 2024

Disclaimer: IMF Working Papers describe research in progress by the author(s) and are published to elicit comments and to encourage debate. The views expressed in IMF Working Papers are those of the author(s) and do not necessarily represent the views of the IMF, its Executive Board, or IMF management.

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.

Subject: GDP forecasting, National accounts

Keywords: Choice matrix p, Covariance matrix, Forecast error, Forecast Reconciliation, GDP forecasting, Hierarchical Time Series, IMF working papers, Lower bound function, Lower bound minimization, Minimum Trace Reconciliation, N×m matrix, Trace reconciliation, Weight matrix

Publication Details

Pages:

12
Volume:

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DOI:

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Issue:

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Series:

Working Paper No. 2022/136
Stock No:

WPIEA2022136
ISBN:

9798400216312
ISSN:

1018-5941

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