IDEAS home Printed from https://ideas.repec.org/a/eee/intfor/v36y2020i1p54-74.html
   My bibliography  Save this article

The M4 Competition: 100,000 time series and 61 forecasting methods

Author

Listed:
  • Makridakis, Spyros
  • Spiliotis, Evangelos
  • Assimakopoulos, Vassilios

Abstract

The M4 Competition follows on from the three previous M competitions, the purpose of which was to learn from empirical evidence both how to improve the forecasting accuracy and how such learning could be used to advance the theory and practice of forecasting. The aim of M4 was to replicate and extend the three previous competitions by: (a) significantly increasing the number of series, (b) expanding the number of forecasting methods, and (c) including prediction intervals in the evaluation process as well as point forecasts. This paper covers all aspects of M4 in detail, including its organization and running, the presentation of its results, the top-performing methods overall and by categories, its major findings and their implications, and the computational requirements of the various methods. Finally, it summarizes its main conclusions and states the expectation that its series will become a testing ground for the evaluation of new methods and the improvement of the practice of forecasting, while also suggesting some ways forward for the field.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:intfor:v:36:y:2020:i:1:p:54-74
    DOI: 10.1016/j.ijforecast.2019.04.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0169207019301128
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ijforecast.2019.04.014?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. Crone, Sven F. & Hibon, Michèle & Nikolopoulos, Konstantinos, 2011. "Advances in forecasting with neural networks? Empirical evidence from the NN3 competition on time series prediction," International Journal of Forecasting, Elsevier, vol. 27(3), pages 635-660.
    2. Smyl, Slawek, 2020. "A hybrid method of exponential smoothing and recurrent neural networks for time series forecasting," International Journal of Forecasting, Elsevier, vol. 36(1), pages 75-85.
    3. Moore, Geoffrey H. & Boehm, Ernst A. & Banerji, Anirvan, 1994. "Using economic indicators to reduce risk in stock market investments," International Journal of Forecasting, Elsevier, vol. 10(3), pages 405-417, November.
    4. 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).
    5. Pawlikowski, Maciej & Chorowska, Agata, 2020. "Weighted ensemble of statistical models," International Journal of Forecasting, Elsevier, vol. 36(1), pages 93-97.
    6. Makridakis, Spyros & Hibon, Michele & Lusk, Ed & Belhadjali, Moncef, 1987. "Confidence intervals: An empirical investigation of the series in the M-competition," International Journal of Forecasting, Elsevier, vol. 3(3-4), pages 489-508.
    7. Spiliotis, Evangelos & Nikolopoulos, Konstantinos & Assimakopoulos, Vassilios, 2019. "Tales from tails: On the empirical distributions of forecasting errors and their implication to risk," International Journal of Forecasting, Elsevier, vol. 35(2), pages 687-698.
    8. Hyndman, Rob J. & Koehler, Anne B. & Snyder, Ralph D. & Grose, Simone, 2002. "A state space framework for automatic forecasting using exponential smoothing methods," International Journal of Forecasting, Elsevier, vol. 18(3), pages 439-454.
    9. Fiorucci, Jose A. & Pellegrini, Tiago R. & Louzada, Francisco & Petropoulos, Fotios & Koehler, Anne B., 2016. "Models for optimising the theta method and their relationship to state space models," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1151-1161.
    10. Assimakopoulos, V. & Nikolopoulos, K., 2000. "The theta model: a decomposition approach to forecasting," International Journal of Forecasting, Elsevier, vol. 16(4), pages 521-530.
    11. Makridakis, Spyros & Taleb, Nassim, 2009. "Decision making and planning under low levels of predictability," International Journal of Forecasting, Elsevier, vol. 25(4), pages 716-733, October.
    12. Hyndman, Rob J., 2020. "A brief history of forecasting competitions," International Journal of Forecasting, Elsevier, vol. 36(1), pages 7-14.
    13. Taleb, Nassim Nicholas, 2009. "Errors, robustness, and the fourth quadrant," International Journal of Forecasting, Elsevier, vol. 25(4), pages 744-759, October.
    14. Athanasopoulos, George & Hyndman, Rob J. & Song, Haiyan & Wu, Doris C., 2011. "The tourism forecasting competition," International Journal of Forecasting, Elsevier, vol. 27(3), pages 822-844, July.
    15. Kim, Sungil & Kim, Heeyoung, 2016. "A new metric of absolute percentage error for intermittent demand forecasts," International Journal of Forecasting, Elsevier, vol. 32(3), pages 669-679.
    16. Claeskens, Gerda & Magnus, Jan R. & Vasnev, Andrey L. & Wang, Wendun, 2016. "The forecast combination puzzle: A simple theoretical explanation," International Journal of Forecasting, Elsevier, vol. 32(3), pages 754-762.
    17. Jakubovskis, Aldis, 2017. "Strategic facility location, capacity acquisition, and technology choice decisions under demand uncertainty: Robust vs. non-robust optimization approaches," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1095-1104.
    18. Montero-Manso, Pablo & Athanasopoulos, George & Hyndman, Rob J. & Talagala, Thiyanga S., 2020. "FFORMA: Feature-based forecast model averaging," International Journal of Forecasting, Elsevier, vol. 36(1), pages 86-92.
    19. Makridakis, Spyros & Chatfield, Chris & Hibon, Michele & Lawrence, Michael & Mills, Terence & Ord, Keith & Simmons, LeRoy F., 1993. "The M2-competition: A real-time judgmentally based forecasting study," International Journal of Forecasting, Elsevier, vol. 9(1), pages 5-22, April.
    20. Chan, Felix & Pauwels, Laurent L., 2018. "Some theoretical results on forecast combinations," International Journal of Forecasting, Elsevier, vol. 34(1), pages 64-74.
    21. 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.
    22. Petropoulos, Fotios & Svetunkov, Ivan, 2020. "A simple combination of univariate models," International Journal of Forecasting, Elsevier, vol. 36(1), pages 110-115.
    23. 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.
    24. Ingel, Anti & Shahroudi, Novin & Kängsepp, Markus & Tättar, Andre & Komisarenko, Viacheslav & Kull, Meelis, 2020. "Correlated daily time series and forecasting in the M4 competition," International Journal of Forecasting, Elsevier, vol. 36(1), pages 121-128.
    25. Syntetos, Aris A. & Nikolopoulos, Konstantinos & Boylan, John E., 2010. "Judging the judges through accuracy-implication metrics: The case of inventory forecasting," International Journal of Forecasting, Elsevier, vol. 26(1), pages 134-143, January.
    26. Prak, Dennis & Teunter, Ruud, 2019. "A general method for addressing forecasting uncertainty in inventory models," International Journal of Forecasting, Elsevier, vol. 35(1), pages 224-238.
    27. 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.
    28. Goodwin, Paul & Lawton, Richard, 1999. "On the asymmetry of the symmetric MAPE," International Journal of Forecasting, Elsevier, vol. 15(4), pages 405-408, October.
    29. Jaganathan, Srihari & Prakash, P.K.S., 2020. "A combination-based forecasting method for the M4-competition," International Journal of Forecasting, Elsevier, vol. 36(1), pages 98-104.
    30. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    31. J D Bermúdez & J V Segura & E Vercher, 2010. "Bayesian forecasting with the Holt–Winters model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 164-171, January.
    32. Petropoulos, Fotios & Wang, Xun & Disney, Stephen M., 2019. "The inventory performance of forecasting methods: Evidence from the M3 competition data," International Journal of Forecasting, Elsevier, vol. 35(1), pages 251-265.
    33. Kolassa, Stephan, 2011. "Combining exponential smoothing forecasts using Akaike weights," International Journal of Forecasting, Elsevier, vol. 27(2), pages 238-251, April.
    34. Petropoulos, Fotios & Hyndman, Rob J. & Bergmeir, Christoph, 2018. "Exploring the sources of uncertainty: Why does bagging for time series forecasting work?," European Journal of Operational Research, Elsevier, vol. 268(2), pages 545-554.
    35. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
    36. Hong, Tao & Pinson, Pierre & Fan, Shu & Zareipour, Hamidreza & Troccoli, Alberto & Hyndman, Rob J., 2016. "Probabilistic energy forecasting: Global Energy Forecasting Competition 2014 and beyond," International Journal of Forecasting, Elsevier, vol. 32(3), pages 896-913.
    37. Spyros Makridakis & Robert L. Winkler, 1983. "Averages of Forecasts: Some Empirical Results," Management Science, INFORMS, vol. 29(9), pages 987-996, September.
    38. Makridakis, Spyros & Spiliotis, Evangelos & Assimakopoulos, Vassilios, 2018. "The M4 Competition: Results, findings, conclusion and way forward," International Journal of Forecasting, Elsevier, vol. 34(4), pages 802-808.
    39. Zhang, Guoqiang & Eddy Patuwo, B. & Y. Hu, Michael, 1998. "Forecasting with artificial neural networks:: The state of the art," International Journal of Forecasting, Elsevier, vol. 14(1), pages 35-62, March.
    40. Franses, Philip Hans, 2016. "A note on the Mean Absolute Scaled Error," International Journal of Forecasting, Elsevier, vol. 32(1), pages 20-22.
    41. 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.
    42. Ardia, David & Bluteau, Keven & Boudt, Kris & Catania, Leopoldo, 2018. "Forecasting risk with Markov-switching GARCH models:A large-scale performance study," International Journal of Forecasting, Elsevier, vol. 34(4), pages 733-747.
    43. 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.
    44. Kolassa, Stephan, 2016. "Evaluating predictive count data distributions in retail sales forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 788-803.
    45. Spiliotis, Evangelos & Kouloumos, Andreas & Assimakopoulos, Vassilios & Makridakis, Spyros, 2020. "Are forecasting competitions data representative of the reality?," International Journal of Forecasting, Elsevier, vol. 36(1), pages 37-53.
    46. Makridakis, Spyros & Hogarth, Robin M. & Gaba, Anil, 2009. "Forecasting and uncertainty in the economic and business world," International Journal of Forecasting, Elsevier, vol. 25(4), pages 794-812, October.
    47. 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.
    48. 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.
    49. Jeremy Smith & Kenneth F. Wallis, 2009. "A Simple Explanation of the Forecast Combination Puzzle," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(3), pages 331-355, June.
    50. Koning, Alex J. & Franses, Philip Hans & Hibon, Michele & Stekler, H.O., 2005. "The M3 competition: Statistical tests of the results," International Journal of Forecasting, Elsevier, vol. 21(3), pages 397-409.
    51. Makridakis, Spyros, 1993. "Accuracy measures: theoretical and practical concerns," International Journal of Forecasting, Elsevier, vol. 9(4), pages 527-529, December.
    52. Jose, Victor Richmond R. & Winkler, Robert L., 2008. "Simple robust averages of forecasts: Some empirical results," International Journal of Forecasting, Elsevier, vol. 24(1), pages 163-169.
    53. Kolassa, Stephan, 2011. "Combining exponential smoothing forecasts using Akaike weights," International Journal of Forecasting, Elsevier, vol. 27(2), pages 238-251.
    54. Fiorucci, Jose Augusto & Louzada, Francisco, 2020. "GROEC: Combination method via Generalized Rolling Origin Evaluation," International Journal of Forecasting, Elsevier, vol. 36(1), pages 105-109.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. Spiliotis, Evangelos & Nikolopoulos, Konstantinos & Assimakopoulos, Vassilios, 2019. "Tales from tails: On the empirical distributions of forecasting errors and their implication to risk," International Journal of Forecasting, Elsevier, vol. 35(2), pages 687-698.
    4. Semenoglou, Artemios-Anargyros & Spiliotis, Evangelos & Makridakis, Spyros & Assimakopoulos, Vassilios, 2021. "Investigating the accuracy of cross-learning time series forecasting methods," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1072-1084.
    5. Spiliotis, Evangelos & Assimakopoulos, Vassilios & Makridakis, Spyros, 2020. "Generalizing the Theta method for automatic forecasting," European Journal of Operational Research, Elsevier, vol. 284(2), pages 550-558.
    6. Petropoulos, Fotios & Makridakis, Spyros & Assimakopoulos, Vassilios & Nikolopoulos, Konstantinos, 2014. "‘Horses for Courses’ in demand forecasting," European Journal of Operational Research, Elsevier, vol. 237(1), pages 152-163.
    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. Jennifer L. Castle & Jurgen A. Doornik & David F. Hendry, 2021. "Forecasting Principles from Experience with Forecasting Competitions," Forecasting, MDPI, Open Access Journal, vol. 3(1), pages 1-28, February.
    9. Kourentzes, Nikolaos & Barrow, Devon & Petropoulos, Fotios, 2019. "Another look at forecast selection and combination: Evidence from forecast pooling," International Journal of Production Economics, Elsevier, vol. 209(C), pages 226-235.
    10. Spiliotis, Evangelos & Kouloumos, Andreas & Assimakopoulos, Vassilios & Makridakis, Spyros, 2020. "Are forecasting competitions data representative of the reality?," International Journal of Forecasting, Elsevier, vol. 36(1), pages 37-53.
    11. Jaganathan, Srihari & Prakash, P.K.S., 2020. "A combination-based forecasting method for the M4-competition," International Journal of Forecasting, Elsevier, vol. 36(1), pages 98-104.
    12. Mirakyan, Atom & Meyer-Renschhausen, Martin & Koch, Andreas, 2017. "Composite forecasting approach, application for next-day electricity price forecasting," Energy Economics, Elsevier, vol. 66(C), pages 228-237.
    13. Ji Wu & Xian Cheng & Stephen Shaoyi Liao, 2020. "Tourism forecast combination using the stochastic frontier analysis technique," Tourism Economics, , vol. 26(7), pages 1086-1107, November.
    14. Fiorucci, Jose A. & Pellegrini, Tiago R. & Louzada, Francisco & Petropoulos, Fotios & Koehler, Anne B., 2016. "Models for optimising the theta method and their relationship to state space models," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1151-1161.
    15. Hewamalage, Hansika & Bergmeir, Christoph & Bandara, Kasun, 2021. "Recurrent Neural Networks for Time Series Forecasting: Current status and future directions," International Journal of Forecasting, Elsevier, vol. 37(1), pages 388-427.
    16. Meira, Erick & Cyrino Oliveira, Fernando Luiz & Jeon, Jooyoung, 2021. "Treating and Pruning: New approaches to forecasting model selection and combination using prediction intervals," International Journal of Forecasting, Elsevier, vol. 37(2), pages 547-568.
    17. 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.
    18. Theodosiou, Marina, 2011. "Forecasting monthly and quarterly time series using STL decomposition," International Journal of Forecasting, Elsevier, vol. 27(4), pages 1178-1195, October.
    19. Petropoulos, Fotios & Svetunkov, Ivan, 2020. "A simple combination of univariate models," International Journal of Forecasting, Elsevier, vol. 36(1), pages 110-115.
    20. Fotios Petropoulos & Evangelos Spiliotis, 2021. "The Wisdom of the Data: Getting the Most Out of Univariate Time Series Forecasting," Forecasting, MDPI, Open Access Journal, vol. 3(3), pages 1-20, June.

    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:36:y:2020:i:1:p:54-74. 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: . General contact details of provider: http://www.elsevier.com/locate/ijforecast .

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