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Holt-Winters Forecasting: An Alternative Formulation Applied to UK Air Passenger Data

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  • J. D. Bermudez
  • J. V. Segura
  • E. Vercher

Abstract

This paper provides a formulation for the additive Holt-Winters forecasting procedure that simplifies both obtaining maximum likelihood estimates of all unknowns, smoothing parameters and initial conditions, and the computation of point forecasts and reliable predictive intervals. The stochastic component of the model is introduced by means of additive, uncorrelated, homoscedastic and Normal errors, and then the joint distribution of the data vector, a multivariate Normal distribution, is obtained. In the case where a data transformation was used to improve the fit of the model, cumulative forecasts are obtained here using a Monte-Carlo approximation. This paper describes the method by applying it to the series of monthly total UK air passengers collected by the Civil Aviation Authority, a long time series from 1949 to the present day, and compares the resulting forecasts with those obtained in previous studies.

Suggested Citation

  • J. D. Bermudez & J. V. Segura & E. Vercher, 2007. "Holt-Winters Forecasting: An Alternative Formulation Applied to UK Air Passenger Data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(9), pages 1075-1090.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:9:p:1075-1090
    DOI: 10.1080/02664760701592125
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    References listed on IDEAS

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    1. Peter R. Winters, 1960. "Forecasting Sales by Exponentially Weighted Moving Averages," Management Science, INFORMS, vol. 6(3), pages 324-342, April.
    2. J D Bermúdez & J V Segura & E Vercher, 2006. "Improving demand forecasting accuracy using nonlinear programming software," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(1), pages 94-100, January.
    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. Yar, Mohammed & Chatfield, Chris, 1990. "Prediction intervals for the Holt-Winters forecasting procedure," International Journal of Forecasting, Elsevier, vol. 6(1), pages 127-137.
    5. Koehler, Anne B. & Snyder, Ralph D. & Ord, J. Keith, 2001. "Forecasting models and prediction intervals for the multiplicative Holt-Winters method," International Journal of Forecasting, Elsevier, vol. 17(2), pages 269-286.
    6. Segura, J. V. & Vercher, E., 2001. "A spreadsheet modeling approach to the Holt-Winters optimal forecasting," European Journal of Operational Research, Elsevier, vol. 131(2), pages 375-388, June.
    7. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    8. Grubb, Howard & Mason, Alexina, 2001. "Long lead-time forecasting of UK air passengers by Holt-Winters methods with damped trend," International Journal of Forecasting, Elsevier, vol. 17(1), pages 71-82.
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    Citations

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    Cited by:

    1. Xiao, Yi & Liu, John J. & Hu, Yi & Wang, Yingfeng & Lai, Kin Keung & Wang, Shouyang, 2014. "A neuro-fuzzy combination model based on singular spectrum analysis for air transport demand forecasting," Journal of Air Transport Management, Elsevier, vol. 39(C), pages 1-11.
    2. Jin, Feng & Li, Yongwu & Sun, Shaolong & Li, Hongtao, 2020. "Forecasting air passenger demand with a new hybrid ensemble approach," Journal of Air Transport Management, Elsevier, vol. 83(C).
    3. Guo Rui & Zhong Zhaowei, 2017. "Forecasting the Air Passenger Volume in Singapore: An Evaluation of TimeSeries Models," International Journal of Technology and Engineering Studies, PROF.IR.DR.Mohid Jailani Mohd Nor, vol. 3(3), pages 117-123.
    4. J. Bermúdez & J. Segura & E. Vercher, 2008. "SIOPRED: a prediction and optimisation integrated system for demand," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 258-271, December.
    5. 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.
    6. E. Vercher & A. Corberán-Vallet & J. Segura & J. Bermúdez, 2012. "Initial conditions estimation for improving forecast accuracy in exponential smoothing," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 517-533, July.
    7. Corberán-Vallet, Ana & Bermúdez, José D. & Vercher, Enriqueta, 2011. "Forecasting correlated time series with exponential smoothing models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 252-265.
    8. Nieto, María Rosa & Carmona-Benítez, Rafael Bernardo, 2018. "ARIMA + GARCH + Bootstrap forecasting method applied to the airline industry," Journal of Air Transport Management, Elsevier, vol. 71(C), pages 1-8.
    9. Bermúdez, José D. & Corberán-Vallet, Ana & Vercher, Enriqueta, 2009. "Multivariate exponential smoothing: A Bayesian forecast approach based on simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1761-1769.
    10. José V. Segura-Heras & José D. Bermúdez & Ana Corberán-Vallet & Enriqueta Vercher, 2022. "Analysis of Weighting Strategies for Improving the Accuracy of Combined Forecasts," Mathematics, MDPI, vol. 10(5), pages 1-12, February.
    11. Ayan Chattopadhyay & Somarata Chakraborty, 2019. "Market size growth survival in multi-generation technology environment: A predictive review of the Indian air-conditioner and refrigerator industry," Asian Journal of Empirical Research, Asian Economic and Social Society, vol. 9(5), pages 132-146, May.
    12. de Paula, R.O. & Silva, L.R. & Vilela, M.L. & Cruz, R.O.M., 2019. "Forecasting passenger movement for Brazilian airports network based on the segregation of primary and secondary demand applied to Brazilian civil aviation policies planning," Transport Policy, Elsevier, vol. 77(C), pages 23-29.
    13. 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.
    14. Corberán-Vallet, Ana & Bermúdez, José D. & Vercher, Enriqueta, 2011. "Forecasting correlated time series with exponential smoothing models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 252-265, April.

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