11.8 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.
  • A recent survey of forecast reconciliation is provided by George Athanasopoulos et al. (2020).
  • The reconciliation methods were developed in a series of papers. The later papers summarise previous results and present the most general theory: Wickramasuriya et al. (2019), Panagiotelis et al. (2021), Panagiotelis et al. (2023).
  • G. Athanasopoulos et al. (2017) extends the reconciliation approach to deal with temporal hierarchies.
  • The tourism example is discussed in more detail in G. Athanasopoulos et al. (2009), Wickramasuriya et al. (2019), and Kourentzes & Athanasopoulos (2019).


Athanasopoulos, G., Ahmed, R. A., & Hyndman, R. J. (2009). Hierarchical forecasts for Australian domestic tourism. International Journal of Forecasting, 25, 146–166. [DOI]
Athanasopoulos, George, Gamakumara, P., Panagiotelis, A., Hyndman, R. J., & Affan, M. (2020). Hierarchical forecasting. In P. Fuleky (Ed.), Macroeconomic forecasting in the era of big data (pp. 689–719). Springer. [DOI]
Athanasopoulos, G., Hyndman, R. J., Kourentzes, N., & Petropoulos, F. (2017). Forecasting with temporal hierarchies. European Journal of Operational Research, 262(1), 60–74. [DOI]
Gross, C. W., & Sohl, J. E. (1990). Disaggregation methods to expedite product line forecasting. Journal of Forecasting, 9, 233–254. [DOI]
Kourentzes, N., & Athanasopoulos, G. (2019). Cross-temporal coherent forecasts for Australian tourism. Annals of Tourism Research, 75, 393–409. [DOI]
Panagiotelis, A., Athanasopoulos, G., Gamakumara, P., & Hyndman, R. J. (2021). Forecast reconciliation: A geometric view with new insights on bias correction. International Journal of Forecasting, 37(1), 343–359. [DOI]
Panagiotelis, A., Gamakumara, P., Athanasopoulos, G., & Hyndman, R. J. (2023). Probabilistic forecast reconciliation: Properties, evaluation and score optimisation. European J Operational Research, 306(2), 693–706. [DOI]
Wickramasuriya, S. L., Athanasopoulos, G., & Hyndman, R. J. (2019). Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization. Journal of the American Statistical Association, 114(526), 804–819. [DOI]