IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/66362.html
   My bibliography  Save this paper

Forecasting with Temporal Hierarchies

Author

Listed:
  • Athanasopoulos, George
  • Hyndman, Rob J.
  • Kourentzes, Nikolaos
  • Petropoulos, Fotios

Abstract

This paper introduces the concept of Temporal Hierarchies for time series forecasting. A temporal hierarchy can be constructed for any time series by means of non-overlapping temporal aggregation. Predictions constructed at all aggregation levels are combined with the proposed framework to result in temporally reconciled, accurate and robust forecasts. The implied combination mitigates modelling uncertainty, while the reconciled nature of the forecasts results in a unified prediction that supports aligned decisions at different planning horizons: from short-term operational up to long-term strategic planning. The proposed methodology is independent of forecasting models. It can embed high level managerial forecasts that incorporate complex and unstructured information with lower level statistical forecasts. Our results show that forecasting with temporal hierarchies increases accuracy over conventional forecasting, particularly under increased modelling uncertainty. We discuss organisational implications of the temporally reconciled forecasts using a case study of Accident & Emergency departments.

Suggested Citation

  • Athanasopoulos, George & Hyndman, Rob J. & Kourentzes, Nikolaos & Petropoulos, Fotios, 2015. "Forecasting with Temporal Hierarchies," MPRA Paper 66362, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:66362
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/66362/1/MPRA_paper_66362.pdf
    File Function: original version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Andrea Silvestrini & Matteo Salto & Laurent Moulin & David Veredas, 2008. "Monitoring and forecasting annual public deficit every month: the case of France," Empirical Economics, Springer, vol. 34(3), pages 493-524, June.
    2. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    3. Hyndman, Rob J. & Khandakar, Yeasmin, 2008. "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i03).
    4. Jonathan E. Helm & Mark P. Van Oyen, 2014. "Design and Optimization Methods for Elective Hospital Admissions," Operations Research, INFORMS, vol. 62(6), pages 1265-1282, December.
    5. Andrea Silvestrini & David Veredas, 2008. "Temporal Aggregation Of Univariate And Multivariate Time Series Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 22(3), pages 458-497, July.
    6. Kolassa, Stephan, 2011. "Combining exponential smoothing forecasts using Akaike weights," International Journal of Forecasting, Elsevier, vol. 27(2), pages 238-251, April.
    7. 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.
    8. Andrawis, Robert R. & Atiya, Amir F. & El-Shishiny, Hisham, 2011. "Combination of long term and short term forecasts, with application to tourism demand forecasting," International Journal of Forecasting, Elsevier, vol. 27(3), pages 870-886, July.
    9. Barrow, Devon K. & Kourentzes, Nikolaos, 2016. "Distributions of forecasting errors of forecast combinations: Implications for inventory management," International Journal of Production Economics, Elsevier, vol. 177(C), pages 24-33.
    10. Fotios Petropoulos & Nikolaos Kourentzes, 2015. "Forecast combinations for intermittent demand," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(6), pages 914-924, June.
    11. Min, Chung-ki & Zellner, Arnold, 1993. "Bayesian and non-Bayesian methods for combining models and forecasts with applications to forecasting international growth rates," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 89-118, March.
    12. Hyndman, Rob J. & Ahmed, Roman A. & Athanasopoulos, George & Shang, Han Lin, 2011. "Optimal combination forecasts for hierarchical time series," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2579-2589, September.
    13. Goodwin, Paul, 2000. "Correct or combine? Mechanically integrating judgmental forecasts with statistical methods," International Journal of Forecasting, Elsevier, vol. 16(2), pages 261-275.
    14. Izady, Navid & Worthington, Dave, 2012. "Setting staffing requirements for time dependent queueing networks: The case of accident and emergency departments," European Journal of Operational Research, Elsevier, vol. 219(3), pages 531-540.
    15. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
    16. Rossana, Robert J & Seater, John J, 1995. "Temporal Aggregation and Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(4), pages 441-451, October.
    17. Spyros Makridakis & Robert L. Winkler, 1983. "Averages of Forecasts: Some Empirical Results," Management Science, INFORMS, vol. 29(9), pages 987-996, September.
    18. Ceren Kolsarici & Demetrios Vakratsas, 2015. "Correcting for Misspecification in Parameter Dynamics to Improve Forecast Accuracy with Adaptively Estimated Models," Management Science, INFORMS, vol. 61(10), pages 2495-2513, October.
    19. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    20. Capistrán, Carlos & Timmermann, Allan, 2009. "Forecast Combination With Entry and Exit of Experts," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 428-440.
    21. Robert L. Winkler & Robert T. Clemen, 1992. "Sensitivity of Weights in Combining Forecasts," Operations Research, INFORMS, vol. 40(3), pages 609-614, June.
    22. Andrawis, Robert R. & Atiya, Amir F. & El-Shishiny, Hisham, 2011. "Combination of long term and short term forecasts, with application to tourism demand forecasting," International Journal of Forecasting, Elsevier, vol. 27(3), pages 870-886.
    23. Souza, Leonardo R. & Smith, Jeremy, 2004. "Effects of temporal aggregation on estimates and forecasts of fractionally integrated processes: a Monte-Carlo study," International Journal of Forecasting, Elsevier, vol. 20(3), pages 487-502.
    24. Graham Elliott & Allan Timmermann, 2005. "Optimal Forecast Combination Under Regime Switching ," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(4), pages 1081-1102, November.
    25. Hotta, Luiz Koodi, 1993. "The effect of additive outliers on the estimates from aggregated and disaggregated ARIMA models," International Journal of Forecasting, Elsevier, vol. 9(1), pages 85-93, April.
    26. Yee, C.L. & Platts, K.W., 2006. "A framework and tool for supply network strategy operationalisation," International Journal of Production Economics, Elsevier, vol. 104(1), pages 230-248, November.
    27. Elliott, Graham & Timmermann, Allan, 2004. "Optimal forecast combinations under general loss functions and forecast error distributions," Journal of Econometrics, Elsevier, vol. 122(1), pages 47-79, September.
    28. Apurva Jain & Kamran Moinzadeh & Yong-Pin Zhou, 2012. "A Single-Supplier, Multiple-Retailer Model with Single-Season, Multiple-Ordering Opportunities, and Fixed Ordering Cost," Operations Research, INFORMS, vol. 60(5), pages 1098-1110, October.
    29. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, Elsevier.
    30. 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.
    31. 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.
    32. Alison Hubbard Ashton & Robert H. Ashton, 1985. "Aggregating Subjective Forecasts: Some Empirical Results," Management Science, INFORMS, vol. 31(12), pages 1499-1508, December.
    33. 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.
    34. Tan, Kim Hua & Platts, Ken, 2004. "Operationalising strategy: Mapping manufacturing variables," International Journal of Production Economics, Elsevier, vol. 89(3), pages 379-393, June.
    35. P. J. Lamberson & Scott E. Page, 2012. "Optimal Forecasting Groups," Management Science, INFORMS, vol. 58(4), pages 805-810, April.
    36. Van-Anh Truong, 2015. "Optimal Advance Scheduling," Management Science, INFORMS, vol. 61(7), pages 1584-1597, July.
    37. Kourentzes, Nikolaos & Petropoulos, Fotios, 2016. "Forecasting with multivariate temporal aggregation: The case of promotional modelling," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 145-153.
    38. Kolassa, Stephan, 2011. "Combining exponential smoothing forecasts using Akaike weights," International Journal of Forecasting, Elsevier, vol. 27(2), pages 238-251.
    39. Shanika L Wickramasuriya & George Athanasopoulos & Rob J Hyndman, 2015. "Forecasting hierarchical and grouped time series through trace minimization," Monash Econometrics and Business Statistics Working Papers 15/15, Monash University, Department of Econometrics and Business Statistics.
    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. Shanika L. Wickramasuriya & George Athanasopoulos & Rob J. Hyndman, 2017. "Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization," Monash Econometrics and Business Statistics Working Papers 22/17, Monash University, Department of Econometrics and Business Statistics.
    2. repec:eee:insuma:v:75:y:2017:i:c:p:166-179 is not listed on IDEAS
    3. Puwasala Gamakumara & Anastasios Panagiotelis & George Athanasopoulos & Rob J Hyndman, 2018. "Probabilisitic forecasts in hierarchical time series," Monash Econometrics and Business Statistics Working Papers 11/18, Monash University, Department of Econometrics and Business Statistics.
    4. repec:eee:transe:v:113:y:2018:i:c:p:225-238 is not listed on IDEAS
    5. Shanika L Wickramasuriya & George Athanasopoulos & Rob J Hyndman, 2015. "Forecasting hierarchical and grouped time series through trace minimization," Monash Econometrics and Business Statistics Working Papers 15/15, Monash University, Department of Econometrics and Business Statistics.
    6. repec:eee:ejores:v:269:y:2018:i:3:p:860-869 is not listed on IDEAS

    More about this item

    Keywords

    Hierarchical forecasting; temporal aggregation; reconciliation; forecast combination;

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:pra:mprapa:66362. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.