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Models for optimising the theta method and their relationship to state space models

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  • Fiorucci, Jose A.
  • Pellegrini, Tiago R.
  • Louzada, Francisco
  • Petropoulos, Fotios
  • Koehler, Anne B.

Abstract

Accurate and robust forecasting methods for univariate time series are very important when the objective is to produce estimates for large numbers of time series. In this context, the Theta method’s performance in the M3-Competition caught researchers’ attention. The Theta method, as implemented in the monthly subset of the M3-Competition, decomposes the seasonally adjusted data into two “theta lines”. The first theta line removes the curvature of the data in order to estimate the long-term trend component. The second theta line doubles the local curvatures of the series so as to approximate the short-term behaviour. We provide generalisations of the Theta method. The proposed Dynamic Optimised Theta Model is a state space model that selects the best short-term theta line optimally and revises the long-term theta line dynamically. The superior performance of this model is demonstrated through an empirical application. We relate special cases of this model to state space models for simple exponential smoothing with a drift.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:intfor:v:32:y:2016:i:4:p:1151-1161
    DOI: 10.1016/j.ijforecast.2016.02.005
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    1. Everette S. Gardner, Jr. & Ed. Mckenzie, 1985. "Forecasting Trends in Time Series," Management Science, INFORMS, vol. 31(10), pages 1237-1246, October.
    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. 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.
    4. Assimakopoulos, V. & Nikolopoulos, K., 2000. "The theta model: a decomposition approach to forecasting," International Journal of Forecasting, Elsevier, vol. 16(4), pages 521-530.
    5. Dimitrios D. Thomakos & Konstantinos Nikolopoulos, 2015. "Forecasting Multivariate Time Series with the Theta Method," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(3), pages 220-229, April.
    6. 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.
    7. Boylan, John E. & Goodwin, Paul & Mohammadipour, Maryam & Syntetos, Aris A., 2015. "Reproducibility in forecasting research," International Journal of Forecasting, Elsevier, vol. 31(1), pages 79-90.
    8. 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.
    9. Goodwin, Paul & Lawton, Richard, 1999. "On the asymmetry of the symmetric MAPE," International Journal of Forecasting, Elsevier, vol. 15(4), pages 405-408, October.
    10. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    11. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
    12. Hyndman, Rob J. & Billah, Baki, 2003. "Unmasking the Theta method," International Journal of Forecasting, Elsevier, vol. 19(2), pages 287-290.
    13. Spyros Makridakis & Robert L. Winkler, 1983. "Averages of Forecasts: Some Empirical Results," Management Science, INFORMS, vol. 29(9), pages 987-996, September.
    14. 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.
    15. 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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