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   <subfield code="a">Ando, Sakai.</subfield>
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  <datafield tag="245" ind1="1" ind2="3">
   <subfield code="a">An Alternative Proof of Minimum Trace Reconciliation /</subfield>
   <subfield code="c">Sakai Ando, Futoshi Narita.</subfield>
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   <subfield code="a">Washington, D.C. :</subfield>
   <subfield code="b">International Monetary Fund,</subfield>
   <subfield code="c">2022.</subfield>
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   <subfield code="a">IMF Working Papers</subfield>
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   <subfield code="a">&lt;strong&gt;On-Campus Access:&lt;/strong&gt; No User ID or Password Required</subfield>
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   <subfield code="a">Electronic access restricted to authorized BRAC University faculty, staff and students</subfield>
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   <subfield code="a">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.</subfield>
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   <subfield code="a">Mode of access: Internet</subfield>
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  <datafield tag="650" ind1=" " ind2="7">
   <subfield code="a">Forecast Reconciliation</subfield>
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   <subfield code="a">Minimum Trace Reconciliation</subfield>
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   <subfield code="a">IMF Working Papers; Working Paper ;</subfield>
   <subfield code="v">No. 2022/136</subfield>
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