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Reconciling hierarchical forecasts requires estimating the covariance matrix of the residuals, usually done by shrinking the off-diagonal elements of the sample covariance matrix. We propose a novel Double Shrinkage estimator (DS), which incorporates conditional dependence information suggested by the hierarchical structure. To validate these dependency assumptions, we analyze real datasets. Additionally, we evaluate the effectiveness of DS both in covariance matrix estimation and in forecast reconciliation.

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A Novel Shrinkage Estimator of the Covariance Matrix for Hierarchical Time Series

  • 会议论文

  • 发表日期：

    2025年

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  • Chiara Carrara,
  • Lorenzo Zambon,
  • Dario Azzimonti,
  • Giorgio Corani

摘要

Reconciling hierarchical forecasts requires estimating the covariance matrix of the residuals, usually done by shrinking the off-diagonal elements of the sample covariance matrix. We propose a novel Double Shrinkage estimator (DS), which incorporates conditional dependence information suggested by the hierarchical structure. To validate these dependency assumptions, we analyze real datasets. Additionally, we evaluate the effectiveness of DS both in covariance matrix estimation and in forecast reconciliation.