Fast computation of reconciled forecasts for hierarchical and grouped time series

Robin John Hyndman, Alan J Lee, Yiru Earo Wang

Research output: Contribution to journalArticleResearchpeer-review

92 Citations (Scopus)


It is shown that the least squares approach to reconciling hierarchical time series forecasts can be extended to much more general collections of time series with aggregation constraints. The constraints arise due to the need for forecasts of collections of time series to add up in the same way as the observed time series. It is also shown that the computations involved can be handled efficiently by exploiting the structure of the associated design matrix, or by using sparse matrix routines. The proposed algorithms make forecast reconciliation feasible in business applications involving very large numbers of time series.
Original languageEnglish
Pages (from-to)16 - 32
Number of pages17
JournalComputational Statistics and Data Analysis
Publication statusPublished - 2016


  • combining forecasts
  • grouped time series
  • hierarchical time series
  • reconciling forecasts
  • weighted least squares

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