Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Forecasting with a combined model of ETS and ARIMA

  • Jiu Oh (Department of Applied Statistics, Chung-Ang University) ;
  • Byeongchan Seong (Department of Applied Statistics, Chung-Ang University)
  • Received : 2023.09.26
  • Accepted : 2023.11.27
  • Published : 2024.01.31
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Abstract

This paper considers a combined model of exponential smoothing (ETS) and autoregressive integrated moving average (ARIMA) models that are commonly used to forecast time series data. The combined model is constructed through an innovational state space model based on the level variable instead of the differenced variable, and the identifiability of the model is investigated. We consider the maximum likelihood estimation for the model parameters and suggest the model selection steps. The forecasting performance of the model is evaluated by two real time series data. We consider the three competing models; ETS, ARIMA and the trigonometric Box-Cox autoregressive and moving average trend seasonal (TBATS) models, and compare and evaluate their root mean squared errors and mean absolute percentage errors for accuracy. The results show that the combined model outperforms the competing models.

Keywords

Acknowledgement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2022R1F1A1074340).

References

  1. Box GEP and Jenkins GM (1976). Time Series Analysis: Forecasting and Control, Holden-Day, San Francisco.
  2. Campagnoli P, Petrone S, and Petris G (2009). Dynamic Linear Models with R, Springer New York, New York.
  3. De Livera AM, Hyndman RJ, and Snyder RD (2011). Forecasting time series with complex seasonal patterns using exponential smoothing, Journal of the American Statistical Association, 106, 1513-1527. https://doi.org/10.1198/jasa.2011.tm09771
  4. Gardner ES (1985). Exponential smoothing: The state of the art, Journal of Forecasting, 4, 1-28. https://doi.org/10.1002/for.3980040103
  5. Gardner ES (2006). Exponential smoothing: The state of the art-Part II, Journal of Forecasting, 22, 637-666. https://doi.org/10.1016/j.ijforecast.2006.03.005
  6. Hyndman RJ, Athanasopoulos G, Bergmeir C et al. (2023). Forecast: Forecasting Functions for Time Series and Linear Models, R package version 8.21.1, Available from: https://cran.r-project.org/web/packages/forecast/forecast.pdf, https://researchportal.bath.ac.uk/en/publications/forecast-foreca sting-functions-for-time-series-and-linear-models
  7. Hyndman RJ, Koehler AB, Ord JK, and Snyder RD (2008). Forecasting with Exponential Smoothing: The State Space Approach, Springer Berlin, Heidelberg.
  8. Hyndman RJ, Koehler AB, Snyder RD, and Grose S (2002). A state space framework for automatic forecasting using exponential smoothing methods, International Journal of Forecasting, 18, 439-454. https://doi.org/10.1016/S0169-2070(01)00110-8
  9. Lee S and Seong B (2022). Performance for simple combinations of univariate forecasting models, The Korean Journal of Applied Statistics, 35, 385-393. https://doi.org/10.5351/KJAS.2022.35.3.385
  10. Seong B (2020). Smoothing and forecasting mixed-frequency time series with vector exponential smoothing models, Economic Modelling, 91, 463-468. https://doi.org/10.1016/j.econmod.2020.06.020
  11. Svetunkov I (2017). Statistical models underlying functions of 'smooth' package for R, Working Paper of Department of Management Science, Lancaster University 2017:1, 1-52, Available from: https://eprints.lancs.ac.uk/id/eprint/85045/
  12. Svetunkov I (2022b). Smooth: Forecasting Using State Space Models, R package version 3.2.0, Available from: https://cran.r-project.org/web/packages/smooth/index.html, https://arxiv.org/abs/2301.01790
  13. Svetunkov I (2023). Forecasting and Analytics with the Augmented Dynamic Adaptive Model (ADAM), Chapman and Hall/CRC, Florida.
  14. Taylor JW (2003). Short-term electricity demand forecasting using double seasonal exponential smoothing, Journal of the Operational Research Society, 54, 799-805. https://doi.org/10.1057/palgrave.jors.2601589