Cover IMF Working Papers
Buy Book in Print
An Alternative Proof of Minimum Trace Reconciliation
Author:
Mr. Sakai Ando
Search for other papers by Mr. Sakai Ando in
Current site
Google Scholar Close
https://orcid.org/0000-0003-2785-4375
and
Mr. Futoshi Narita
Search for other papers by Mr. Futoshi Narita in
Current site
Google Scholar Close
Series:
IMF Working Papers
Volume/Issue:
Volume 2022: Issue 136
Language:
English
Publication Date:
08 Jul 2022
DOI:
https://doi.org/10.5089/9798400216312.001
ISBN:
9798400216374
ISSN:
1018-5941
Pages:
12
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
Legal-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.
Download PDF (2.1 MB) Download Epub
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.
  • Collapse
  • Expand
Cover IMF Working Papers
IMF Working Papers
ISSN:
1018-5941
Publisher:
International Monetary Fund