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 & 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 et al. (2009), Hyndman, Lee, & Wang (2016), Wickramasuriya et al. (2018).
  • Athanasopoulos, Hyndman, Kourentzes, & Petropoulos (2017) extends the reconciliation approach to deal with temporal hierarchies.


Athanasopoulos, G., Ahmed, R. A., & Hyndman, R. J. (2009). Hierarchical forecasts for Australian domestic tourism. International Journal of Forecasting, 25, 146–166. https://robjhyndman.com/publications/hierarchical-tourism/

Athanasopoulos, G., Hyndman, R. J., Kourentzes, N., & Petropoulos, F. (2017). Forecasting with temporal hierarchies. European Journal of Operational Research, 262(1), 60–74. https://robjhyndman.com/publications/temporal-hierarchies/

Gross, C. W., & Sohl, J. E. (1990). Disaggregation methods to expedite product line forecasting. Journal of Forecasting, 9, 233–254. https://doi.org/10.1002/for.3980090304

Hyndman, R. J., Ahmed, R. A., Athanasopoulos, G., & Shang, H. L. (2011). Optimal combination forecasts for hierarchical time series. Computational Statistics and Data Analysis, 55(9), 2579–2589. https://robjhyndman.com/publications/hierarchical/

Hyndman, R. J., Lee, A., & Wang, E. (2016). Fast computation of reconciled forecasts for hierarchical and grouped time series. Computational Statistics and Data Analysis, 97, 16–32. https://robjhyndman.com/publications/hgts/

Wickramasuriya, S. L., Athanasopoulos, G., & Hyndman, R. J. (2018). Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization. J American Statistical Association, to appear. https://robjhyndman.com/publications/mint/