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Generalizing the Theta method for automatic forecasting

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

Abstract

The Theta method became popular due to its superior performance in the M3 forecasting competition. Since then, although it has been shown that Theta provides accurate forecasts for various types of data, being a solid benchmark to beat, limited research has been conducted to exploit its full potential and generalize its reach. This paper examines three extensions on Theta’s framework to boost its performance. This includes (i) considering both linear and non-linear trends, (ii) allowing to adjust the slope of such trends, and (iii) introducing a multiplicative expression of the underlying forecasting model along with the existing, additive one. The proposed modifications transform Theta into a generalized forecasting algorithm, suitable for automatic time series predictions. The proposed algorithm is evaluated using the series of the M, M3, and M4 competitions. Such an evaluation shows that the proposed approach produces more accurate forecasts than the original, classic Theta, both in terms of point forecasts and prediction intervals, and is also more accurate than other well-known methods for yearly series.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:284:y:2020:i:2:p:550-558
    DOI: 10.1016/j.ejor.2020.01.007
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    1. Spiliotis, Evangelos & Assimakopoulos, Vassilios & Nikolopoulos, Konstantinos, 2019. "Forecasting with a hybrid method utilizing data smoothing, a variation of the Theta method and shrinkage of seasonal factors," International Journal of Production Economics, Elsevier, vol. 209(C), pages 92-102.
    2. 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).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Assimakopoulos, V. & Nikolopoulos, K., 2000. "The theta model: a decomposition approach to forecasting," International Journal of Forecasting, Elsevier, vol. 16(4), pages 521-530.
    9. Cang, Shuang & Yu, Hongnian, 2014. "A combination selection algorithm on forecasting," European Journal of Operational Research, Elsevier, vol. 234(1), pages 127-139.
    10. 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.
    11. Seaman, Brian, 2018. "Considerations of a retail forecasting practitioner," International Journal of Forecasting, Elsevier, vol. 34(4), pages 822-829.
    12. Armstrong, J. Scott & Green, Kesten C. & Graefe, Andreas, 2015. "Golden rule of forecasting: Be conservative," Journal of Business Research, Elsevier, vol. 68(8), pages 1717-1731.
    13. 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.
    14. Ivan Svetunkov & Fotios Petropoulos, 2018. "Old dog, new tricks: a modelling view of simple moving averages," International Journal of Production Research, Taylor & Francis Journals, vol. 56(18), pages 6034-6047, September.
    15. 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.
    16. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    17. Taylor, James W., 2007. "Forecasting daily supermarket sales using exponentially weighted quantile regression," European Journal of Operational Research, Elsevier, vol. 178(1), pages 154-167, April.
    18. 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.
    19. 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.
    20. Hyndman, Rob J. & Billah, Baki, 2003. "Unmasking the Theta method," International Journal of Forecasting, Elsevier, vol. 19(2), pages 287-290.
    21. 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.
    22. 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.
    23. 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.
    24. Babai, Zied & Boylan, John E. & Kolassa, Stephan & Nikolopoulos, Konstantinos, 2016. "Supply chain forecasting: Theory, practice, their gap and the futureAuthor-Name: Syntetos, Aris A," European Journal of Operational Research, Elsevier, vol. 252(1), pages 1-26.
    25. 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.
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    Cited by:

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    2. Aleksandr N. Grekov & Elena V. Vyshkvarkova & Aleksandr S. Mavrin, 2024. "Forecasting and Anomaly Detection in BEWS: Comparative Study of Theta, Croston, and Prophet Algorithms," Forecasting, MDPI, vol. 6(2), pages 1-14, May.
    3. Evangelos Spiliotis & Fotios Petropoulos & Konstantinos Nikolopoulos, 2020. "The Impact of Imperfect Weather Forecasts on Wind Power Forecasting Performance: Evidence from Two Wind Farms in Greece," Energies, MDPI, vol. 13(8), pages 1-18, April.
    4. 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.
    5. 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.
    6. Kang, Yanfei & Cao, Wei & Petropoulos, Fotios & Li, Feng, 2022. "Forecast with forecasts: Diversity matters," European Journal of Operational Research, Elsevier, vol. 301(1), pages 180-190.
    7. Sbrana, Giacomo & Silvestrini, Andrea, 2023. "The RWDAR model: A novel state-space approach to forecasting," International Journal of Forecasting, Elsevier, vol. 39(2), pages 922-937.

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