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An Alternative Proof of Minimum Trace Reconciliation

Author

Listed:
  • Sakai Ando

    (Research Department, International Monetary Fund, 700 19th St NW, Washington, DC 20431, USA)

  • Futoshi Narita

    (Research Department, International Monetary Fund, 700 19th St NW, Washington, DC 20431, USA)

Abstract

Minimum trace reconciliation, developed by Wickramasuriya et al., 2019, is an innovation in the literature on forecast reconciliation. The proof, however, has a gap, and the idea is not easy to extend to more general situations. This paper fills the gap by providing an alternative proof based on the first-order condition in the space of a non-square matrix and arguing 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.

Suggested Citation

  • Sakai Ando & Futoshi Narita, 2024. "An Alternative Proof of Minimum Trace Reconciliation," Forecasting, MDPI, vol. 6(2), pages 1-6, June.
    • Handle: RePEc:gam:jforec:v:6:y:2024:i:2:p:25-461:d:1417163
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    References listed on IDEAS

    as
    1. Shanika L. Wickramasuriya & George Athanasopoulos & Rob J. Hyndman, 2019. "Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series Through Trace Minimization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 804-819, April.
    2. Souhaib Ben Taieb & James W. Taylor & Rob J. Hyndman, 2021. "Hierarchical Probabilistic Forecasting of Electricity Demand With Smart Meter Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 27-43, March.
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