Forecast reconciliation


7 November 2023




9am UTC+11, November 7, 10, 14, 17

Available to IIF members only

Distinguished Lecture Series for the International Institute of Forecasters


It is common to forecast at different levels of aggregation. For example, a retail company will want national forecasts, state forecasts, and store-level forecasts. And they will want them for all products, for groups of products, and for individual products. It is natural to want the forecasts to be “coherent” — that is, that the forecasts add up in the same way as the data. For example, forecasts of regional sales should add up to forecasts of state sales, which should in turn add up to give a forecast for national sales. Coherent forecasts are needed to allow effective planning, such as the allocation of resources across an organization based on forecasts of sales. Coherent forecasts are also more accurate than incoherent forecasts.

Over the past 15 years, forecast reconciliation methods have been developed to ensure forecasts are coherent. Forecasts at all levels of aggregation are produced, and the results are “reconciled” so they are consistent with each other.

I will provide an up-to-date overview of this area, and show how reconciliation methods can lead to better forecasts and better forecasting practices.


(Click title for slides)

  1. Hierarchical time series and forecast reconciliation

    • Hyndman et al. (2011)
    • Wickramasuriya, Athanasopoulos, and Hyndman (2019)
    • Hyndman, Lee, and Wang (2016)
  2. Perspectives on forecast reconciliation

    • Di Fonzo and Girolimetto (2022)
    • Panagiotelis et al. (2021)
    • Wickramasuriya (2021)
    • van Erven and Cugliari (2015)
    • Ben Taieb and Koo (2019)
    • Wickramasuriya, Turlach, and Hyndman (2020)
    • Zhang et al. (2022)
    • Ashouri, Hyndman, and Shmueli (2022)
    • Spiliotis et al. (2021)
  3. Probabilistic forecast reconciliation

    • Ben Taieb, Taylor, and Hyndman (2021)
    • Panagiotelis et al. (2023)
    • Corani, Azzimonti, and Rubattu (2023)
    • Rostami-Tabar and Hyndman (2023)
  4. Temporal and cross-temporal forecast reconciliation

    • Athanasopoulos et al. (2017)
    • Di Fonzo and Girolimetto (2023)
    • Girolimetto et al. (2023)


Review paper

Athansopoulos, Hyndman, Kourentzes & Panagiotelis (2024) “Forecast reconcilation: a review”, International Journal of Forecasting, to appear.

YouTube videos

YouTube videos of all talks are on the IIF channel


Ashouri, Mahsa, Rob J Hyndman, and Galit Shmueli. 2022. “Fast Forecast Reconciliation Using Linear Models.” J Computational & Graphical Statistics 31 (1): 263–82.
Athanasopoulos, George, Rob J Hyndman, Nikolaos Kourentzes, and Fotios Petropoulos. 2017. “Forecasting with Temporal Hierarchies.” European J Operational Research 262 (1): 60–74.
Ben Taieb, Souhaib, and Bonsoo Koo. 2019. “Regularized Regression for Hierarchical Forecasting Without Unbiasedness Conditions.” In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 1337–47. KDD ’19. New York, NY, USA: Association for Computing Machinery.
Ben Taieb, Souhaib, James W Taylor, and Rob J Hyndman. 2021. “Hierarchical Probabilistic Forecasting of Electricity Demand with Smart Meter Data.” J American Statistical Association 116 (533): 27–43.
Corani, Giorgio, Dario Azzimonti, and Nicolo Rubattu. 2023. “Probabilistic Reconciliation of Count Time Series.” International Journal of Forecasting.
Di Fonzo, Tommaso, and Daniele Girolimetto. 2022. “Forecast Combination-Based Forecast Reconciliation: Insights and Extensions.” International Journal of Forecasting forthcoming.
———. 2023. “Cross-Temporal Forecast Reconciliation: Optimal Combination Method and Heuristic Alternatives.” International Journal of Forecasting 39 (1): 39–57.
Girolimetto, Daniele, George Athanasopoulos, Tommaso Di Fonzo, and Rob J Hyndman. 2023. “Cross-Temporal Probabilistic Forecast Reconciliation.”
Hyndman, Rob J, Roman A Ahmed, George Athanasopoulos, and Han Lin Shang. 2011. “Optimal Combination Forecasts for Hierarchical Time Series.” Computational Statistics & Data Analysis 55 (9): 2579–89.
Hyndman, Rob J, Alan Lee, and Earo Wang. 2016. “Fast Computation of Reconciled Forecasts for Hierarchical and Grouped Time Series.” Computational Statistics & Data Analysis 97: 16–32.
Panagiotelis, Anastasios, Puwasala Gamakumara, George Athanasopoulos, and Rob J Hyndman. 2021. “Forecast Reconciliation: A Geometric View with New Insights on Bias Correction.” International J Forecasting 37 (1): 343–59.
———. 2023. “Probabilistic Forecast Reconciliation: Properties, Evaluation and Score Optimisation.” European J Operational Research 306 (2): 693–706.
Rostami-Tabar, Bahman, and Rob J Hyndman. 2023. “Hierarchical Time Series Forecasting in Emergency Medical Services.”
Spiliotis, Evangelos, Mahdi Abolghasemi, Rob J Hyndman, Fotios Petropoulos, and Vassilios Assimakopoulos. 2021. “Hierarchical Forecast Reconciliation with Machine Learning.” Applied Soft Computing 112: 107756.
van Erven, Tim, and Jairo Cugliari. 2015. “Game-Theoretically Optimal Reconciliation of Contemporaneous Hierarchical Time Series Forecasts.” In Modeling and Stochastic Learning for Forecasting in High Dimension, edited by Anestis Antoniadis, Jean-Michel Poggi, and Xavier Brossat, 297–317. Cham: Springer International Publishing.
Wickramasuriya, Shanika L. 2021. “Properties of Point Forecast Reconciliation Approaches.” arXiv Preprint arXiv:2103.11129.
Wickramasuriya, Shanika L, George Athanasopoulos, and Rob J Hyndman. 2019. “Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series Through Trace Minimization.” J American Statistical Association 114 (526): 804–19.
Wickramasuriya, Shanika L, Berwin A Turlach, and Rob J Hyndman. 2020. “Optimal Non-Negative Forecast Reconciliation.” Statistics & Computing 30 (5): 1167–82.
Zhang, Bohan, Yanfei Kang, Anastasios Panagiotelis, and Feng Li. 2022. “Optimal Reconciliation with Immutable Forecasts.” European Journal of Operational Research forthcoming.