IDEAS home Printed from https://ideas.repec.org/a/eee/intfor/v39y2023i4p1502-1511.html
   My bibliography  Save this article

On the evaluation of hierarchical forecasts

Author

Listed:
  • Athanasopoulos, George
  • Kourentzes, Nikolaos

Abstract

The aim of this paper is to provide a thinking road-map and a practical guide to researchers and practitioners working on hierarchical forecasting problems. Evaluating the performance of hierarchical forecasts comes with new challenges stemming from both the structure of the hierarchy and the application context. We discuss several relevant dimensions for researchers and analysts: the scale and units of the time series, the issue of intermittency, the forecast horizon, the importance of multiple evaluation windows and the multiple objective decision context. We conclude with a series of practical recommendations.

Suggested Citation

  • Athanasopoulos, George & Kourentzes, Nikolaos, 2023. "On the evaluation of hierarchical forecasts," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1502-1511.
  • Handle: RePEc:eee:intfor:v:39:y:2023:i:4:p:1502-1511
    DOI: 10.1016/j.ijforecast.2022.08.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0169207022001121
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ijforecast.2022.08.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kourentzes, Nikolaos & Trapero, Juan R. & Barrow, Devon K., 2020. "Optimising forecasting models for inventory planning," International Journal of Production Economics, Elsevier, vol. 225(C).
    2. Kourentzes, Nikolaos & Athanasopoulos, George, 2019. "Cross-temporal coherent forecasts for Australian tourism," Annals of Tourism Research, Elsevier, vol. 75(C), pages 393-409.
    3. Deepak Gupta & Mahardhika Pratama & Zhenyuan Ma & Jun Li & Mukesh Prasad, 2019. "Financial time series forecasting using twin support vector regression," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-27, March.
    4. Jeon, Jooyoung & Panagiotelis, Anastasios & Petropoulos, Fotios, 2019. "Probabilistic forecast reconciliation with applications to wind power and electric load," European Journal of Operational Research, Elsevier, vol. 279(2), pages 364-379.
    5. Kourentzes, Nikolaos & Saayman, Andrea & Jean-Pierre, Philippe & Provenzano, Davide & Sahli, Mondher & Seetaram, Neelu & Volo, Serena, 2021. "Visitor arrivals forecasts amid COVID-19: A perspective from the Africa team," Annals of Tourism Research, Elsevier, vol. 88(C).
    6. Gneiting, Tilmann, 2011. "Quantiles as optimal point forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 197-207.
    7. Kourentzes, Nikolaos & Petropoulos, Fotios & Trapero, Juan R., 2014. "Improving forecasting by estimating time series structural components across multiple frequencies," International Journal of Forecasting, Elsevier, vol. 30(2), pages 291-302.
    8. Shanika L. Wickramasuriya & George Athanasopoulos & Rob J. Hyndman, 2019. "Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series Through Trace Minimization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 804-819, April.
    9. Trapero, Juan R. & Pedregal, Diego J. & Fildes, R. & Kourentzes, N., 2013. "Analysis of judgmental adjustments in the presence of promotions," International Journal of Forecasting, Elsevier, vol. 29(2), pages 234-243.
    10. Panagiotelis, Anastasios & Athanasopoulos, George & Gamakumara, Puwasala & Hyndman, Rob J., 2021. "Forecast reconciliation: A geometric view with new insights on bias correction," International Journal of Forecasting, Elsevier, vol. 37(1), pages 343-359.
    11. Athanasopoulos, George & Ahmed, Roman A. & Hyndman, Rob J., 2009. "Hierarchical forecasts for Australian domestic tourism," International Journal of Forecasting, Elsevier, vol. 25(1), pages 146-166.
    12. Athanasopoulos, George & Hyndman, Rob J. & Kourentzes, Nikolaos & Petropoulos, Fotios, 2017. "Forecasting with temporal hierarchies," European Journal of Operational Research, Elsevier, vol. 262(1), pages 60-74.
    13. Yves R. Sagaert & El-Houssaine Aghezzaf & Nikolaos Kourentzes & Bram Desmet, 2018. "Temporal Big Data for Tactical Sales Forecasting in the Tire Industry," Interfaces, INFORMS, vol. 48(2), pages 121-129, April.
    14. Davydenko, Andrey & Fildes, Robert, 2013. "Measuring forecasting accuracy: The case of judgmental adjustments to SKU-level demand forecasts," International Journal of Forecasting, Elsevier, vol. 29(3), pages 510-522.
    15. Nystrup, Peter & Lindström, Erik & Pinson, Pierre & Madsen, Henrik, 2020. "Temporal hierarchies with autocorrelation for load forecasting," European Journal of Operational Research, Elsevier, vol. 280(3), pages 876-888.
    16. Kourentzes, Nikolaos & Athanasopoulos, George, 2021. "Elucidate structure in intermittent demand series," European Journal of Operational Research, Elsevier, vol. 288(1), pages 141-152.
    17. Stephan Kolassa & Wolfgang Schütz, 2007. "Advantages of the MAD/Mean Ratio over the MAPE," Foresight: The International Journal of Applied Forecasting, International Institute of Forecasters, issue 6, pages 40-43, Spring.
    18. Nikolaos Kourentzes & Dong Li & Arne K. Strauss, 2019. "Unconstraining methods for revenue management systems under small demand," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 18(1), pages 27-41, February.
    19. George Athanasopoulos & Nikolaos Kourentzes, 2020. "On the Evaluation of Hierarchical Forecasts," Monash Econometrics and Business Statistics Working Papers 2/20, Monash University, Department of Econometrics and Business Statistics.
    20. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    21. Tashman, Leonard J., 2000. "Out-of-sample tests of forecasting accuracy: an analysis and review," International Journal of Forecasting, Elsevier, vol. 16(4), pages 437-450.
    22. Gneiting, Tilmann, 2011. "Quantiles as optimal point forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 197-207, April.
    23. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
    24. Abbas,Ali E., 2018. "Foundations of Multiattribute Utility," Cambridge Books, Cambridge University Press, number 9781107150904, September.
    25. R Fildes & B Kingsman, 2011. "Incorporating demand uncertainty and forecast error in supply chain planning models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(3), pages 483-500, March.
    26. Makridakis, Spyros & Spiliotis, Evangelos & Assimakopoulos, Vassilios, 2020. "The M4 Competition: 100,000 time series and 61 forecasting methods," International Journal of Forecasting, Elsevier, vol. 36(1), pages 54-74.
    27. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    28. Saoud, Patrick & Kourentzes, Nikolaos & Boylan, John E., 2022. "Approximations for the Lead Time Variance: a Forecasting and Inventory Evaluation," Omega, Elsevier, vol. 110(C).
    29. Kourentzes, Nikolaos, 2014. "On intermittent demand model optimisation and selection," International Journal of Production Economics, Elsevier, vol. 156(C), pages 180-190.
    30. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    31. Kolassa, Stephan, 2016. "Evaluating predictive count data distributions in retail sales forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 788-803.
    32. Sanders, Nada R. & Graman, Gregory A., 2009. "Quantifying costs of forecast errors: A case study of the warehouse environment," Omega, Elsevier, vol. 37(1), pages 116-125, February.
    33. Armstrong, J. Scott & Collopy, Fred, 1992. "Error measures for generalizing about forecasting methods: Empirical comparisons," International Journal of Forecasting, Elsevier, vol. 8(1), pages 69-80, June.
    34. Fildes, Robert, 1992. "The evaluation of extrapolative forecasting methods," International Journal of Forecasting, Elsevier, vol. 8(1), pages 81-98, June.
    35. Lei Dong & Peng Wang & Fang Yan, 2019. "Damage forecasting based on multi-factor fuzzy time series and cloud model," Journal of Intelligent Manufacturing, Springer, vol. 30(2), pages 521-538, February.
    36. Pritularga, Kandrika F. & Svetunkov, Ivan & Kourentzes, Nikolaos, 2021. "Stochastic coherency in forecast reconciliation," International Journal of Production Economics, Elsevier, vol. 240(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Athanasopoulos, George & Hyndman, Rob J. & Kourentzes, Nikolaos & Panagiotelis, Anastasios, 2024. "Forecast reconciliation: A review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 430-456.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. George Athanasopoulos & Nikolaos Kourentzes, 2021. "On the Evaluation of Hierarchical Forecasts," Monash Econometrics and Business Statistics Working Papers 10/21, Monash University, Department of Econometrics and Business Statistics.
    2. George Athanasopoulos & Nikolaos Kourentzes, 2020. "On the Evaluation of Hierarchical Forecasts," Monash Econometrics and Business Statistics Working Papers 2/20, Monash University, Department of Econometrics and Business Statistics.
    3. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    4. Kourentzes, Nikolaos & Athanasopoulos, George, 2021. "Elucidate structure in intermittent demand series," European Journal of Operational Research, Elsevier, vol. 288(1), pages 141-152.
    5. Athanasopoulos, George & Hyndman, Rob J. & Kourentzes, Nikolaos & Panagiotelis, Anastasios, 2024. "Forecast reconciliation: A review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 430-456.
    6. Pritularga, Kandrika F. & Svetunkov, Ivan & Kourentzes, Nikolaos, 2021. "Stochastic coherency in forecast reconciliation," International Journal of Production Economics, Elsevier, vol. 240(C).
    7. Fildes, Robert & Ma, Shaohui & Kolassa, Stephan, 2022. "Retail forecasting: Research and practice," International Journal of Forecasting, Elsevier, vol. 38(4), pages 1283-1318.
    8. Panagiotelis, Anastasios & Gamakumara, Puwasala & Athanasopoulos, George & Hyndman, Rob J., 2023. "Probabilistic forecast reconciliation: Properties, evaluation and score optimisation," European Journal of Operational Research, Elsevier, vol. 306(2), pages 693-706.
    9. Di Fonzo, Tommaso & Girolimetto, Daniele, 2023. "Cross-temporal forecast reconciliation: Optimal combination method and heuristic alternatives," International Journal of Forecasting, Elsevier, vol. 39(1), pages 39-57.
    10. Di Fonzo, Tommaso & Girolimetto, Daniele, 2024. "Forecast combination-based forecast reconciliation: Insights and extensions," International Journal of Forecasting, Elsevier, vol. 40(2), pages 490-514.
    11. Girolimetto, Daniele & Athanasopoulos, George & Di Fonzo, Tommaso & Hyndman, Rob J., 2024. "Cross-temporal probabilistic forecast reconciliation: Methodological and practical issues," International Journal of Forecasting, Elsevier, vol. 40(3), pages 1134-1151.
    12. Nystrup, Peter & Lindström, Erik & Møller, Jan K. & Madsen, Henrik, 2021. "Dimensionality reduction in forecasting with temporal hierarchies," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1127-1146.
    13. Fotios Petropoulos & Evangelos Spiliotis, 2021. "The Wisdom of the Data: Getting the Most Out of Univariate Time Series Forecasting," Forecasting, MDPI, vol. 3(3), pages 1-20, June.
    14. Spiliotis, Evangelos & Petropoulos, Fotios & Kourentzes, Nikolaos & Assimakopoulos, Vassilios, 2020. "Cross-temporal aggregation: Improving the forecast accuracy of hierarchical electricity consumption," Applied Energy, Elsevier, vol. 261(C).
    15. Corani, Giorgio & Azzimonti, Dario & Rubattu, Nicolò, 2024. "Probabilistic reconciliation of count time series," International Journal of Forecasting, Elsevier, vol. 40(2), pages 457-469.
    16. Makridakis, Spyros & Hyndman, Rob J. & Petropoulos, Fotios, 2020. "Forecasting in social settings: The state of the art," International Journal of Forecasting, Elsevier, vol. 36(1), pages 15-28.
    17. Kang, Yanfei & Spiliotis, Evangelos & Petropoulos, Fotios & Athiniotis, Nikolaos & Li, Feng & Assimakopoulos, Vassilios, 2021. "Déjà vu: A data-centric forecasting approach through time series cross-similarity," Journal of Business Research, Elsevier, vol. 132(C), pages 719-731.
    18. Zhang, Bohan & Kang, Yanfei & Panagiotelis, Anastasios & Li, Feng, 2023. "Optimal reconciliation with immutable forecasts," European Journal of Operational Research, Elsevier, vol. 308(2), pages 650-660.
    19. Panagiotelis, Anastasios & Athanasopoulos, George & Gamakumara, Puwasala & Hyndman, Rob J., 2021. "Forecast reconciliation: A geometric view with new insights on bias correction," International Journal of Forecasting, Elsevier, vol. 37(1), pages 343-359.
    20. Makridakis, Spyros & Spiliotis, Evangelos & Assimakopoulos, Vassilios, 2020. "The M4 Competition: 100,000 time series and 61 forecasting methods," International Journal of Forecasting, Elsevier, vol. 36(1), pages 54-74.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:intfor:v:39:y:2023:i:4:p:1502-1511. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijforecast .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.