10.10 Further reading

Hyndman and Athanasopoulos (2014), Athanasopoulos, Ahmed, and Hyndman (2009) and Gross and Sohl (1990) provide a good introduction to this framework. Wickramasuriya, Athanasopoulos, and Hyndman (2015) provides the latest developments in terms of the optimal reconciliation approach. Athanasopoulos et al. (2017) expands using this framework in the time dimension with temporal hierarchies.


Hyndman, R J, and George Athanasopoulos. 2014. “Optimally Reconciling Forecasts in a Hierarchy.” Foresight: International Journal of Applied Forecasting, no. 35: 42–48.

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

Gross, C W, and J E Sohl. 1990. “Disaggregation methods to expedite product line forecasting.” Journal of Forecasting 9: 233–54.

Wickramasuriya, Shanika L, George Athanasopoulos, and Rob J Hyndman. 2015. “Forecasting Hierarchical and Grouped Time Series Through Trace Minimization.” Working paper 15/15. Monash University Econometrics & Business Statistics.

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