Optimal combination forecasts for hierarchical time series

Rob J. Hyndman*, Roman A. Ahmed, George Athanasopoulos, Han Lin Shang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

226 Citations (Scopus)


In many applications, there are multiple time series that are hierarchically organized and can be aggregated at several different levels in groups based on products, geography or some other features. We call these “hierarchical time series”. They are commonly forecast using either a “bottom-up” or a “top-down” method.

In this paper we propose a new approach to hierarchical forecasting which provides optimal forecasts that are better than forecasts produced by either a top-down or a bottom-up approach. Our method is based on independently forecasting all series at all levels of the hierarchy and then using a regression model to optimally combine and reconcile these forecasts. The resulting revised forecasts add up appropriately across the hierarchy, are unbiased and have minimum variance amongst all combination forecasts under some simple assumptions.

We show in a simulation study that our method performs well compared to the top-down approach and the bottom-up method. We demonstrate our proposed method by forecasting Australian tourism demand where the data are disaggregated by purpose of travel and geographical region.
Original languageEnglish
Pages (from-to)2579-2589
Number of pages21
JournalComputational Statistics and Data Analysis
Issue number9
Publication statusPublished - 1 Sep 2011
Externally publishedYes


  • Bottom-up forecasting
  • Combining forecasts
  • GLS regression
  • Hierarchical forecasting
  • Reconciling forecasts
  • Top-down forecasting


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