10.9 Further reading

There are no other textbooks which cover hierarchical forecasting in any depth, so interested readers will need to tackle the original research papers for further information.

  • Gross and Sohl (1990) provide a good introduction to the top-down approaches.
  • The reconciliation methods were developed in a series of papers, which are best read in the following order: Hyndman et al. (2011), Athanasopoulos, Ahmed, and Hyndman (2009), Hyndman, Lee, and Wang (2016), Wickramasuriya, Athanasopoulos, and Hyndman (2018).
  • Athanasopoulos et al. (2017) extends the reconciliation approach to deal with temporal hierarchies.


Gross, C W, and J E Sohl. 1990. “Disaggregation Methods to Expedite Product Line Forecasting.” Journal of Forecasting 9: 233–54.

Hyndman, Rob J, Roman A Ahmed, George Athanasopoulos, and Han Lin Shang. 2011. “Optimal Combination Forecasts for Hierarchical Time Series.” Computational Statistics and Data Analysis 55 (9): 2579–89. https://doi.org/10.1016/j.csda.2011.03.006.

Athanasopoulos, George, Roman A Ahmed, and Rob J Hyndman. 2009. “Hierarchical Forecasts for Australian Domestic Tourism.” International Journal of Forecasting 25: 146–66. https://doi.org/10.1016/j.ijforecast.2008.07.004.

Hyndman, Rob J, Alan Lee, and Earo Wang. 2016. “Fast Computation of Reconciled Forecasts for Hierarchical and Grouped Time Series.” Computational Statistics and Data Analysis 97: 16–32.

Wickramasuriya, Shanika L, George Athanasopoulos, and Rob J Hyndman. 2018. “Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series Through Trace Minimization.” J American Statistical Association to appear. https://robjhyndman.com/publications/mint/.

Athanasopoulos, George, Rob J Hyndman, Nikolaos Kourentzes, and Fotios Petropoulos. 2017. “Forecasting with Temporal Hierarchies.” European Journal of Operational Research 262 (1): 60–74.