An Alternative Proof of Minimum Trace Reconciliation
IMF Working Papers, July 8, 2022
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- An Alternative Proof of Minimum Trace Reconciliation
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Bibliographic details
- Authors: Sakai Ando, Futoshi Narita
- Published: July 8, 2022
- Series: IMF Working Papers
- DOI: https://doi.org/10.5089/9798400216312.001
Summary
- Minimum trace reconciliation, developed by Wickramasuriya et. al. (2019), is an innovation in the literature of forecast reconciliation.
- The existing proof 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).
- The alternative proof has pedagogical value and connects results in the literature from a unified perspective.
Key Contributions and Findings
- Provides an alternative, simpler proof of Minimum Trace Reconciliation using first-order conditions in the space of non-square matrix.
- Demonstrates extendibility to minimum weighted trace reconciliation results in Panagiotelis et. al. (2021).
- Emphasizes unification of results in forecast reconciliation literature.
Methodology and Technical Focus
- Proof based on first-order condition in the space of non-square matrix.
- Technical concepts and terminology preserved from the source:
- choice matrix p
- covariance matrix
- forecast error
- Forecast Reconciliation
- Hierarchical Time Series
- lower bound function
- lower bound minimization
- Minimum Trace Reconciliation
- n×m matrix
- trace reconciliation
- weight matrix
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- Working Paper