IDEAS home Printed from https://ideas.repec.org/a/jof/jforec/v28y2009i3p218-234.html
   My bibliography  Save this article

A new Bayesian formulation for Holt's exponential smoothing

Author

Listed:
  • Robert R. Andrawis

    (Data Mining Center of Excellence, MCIT, Cairo, Egypt)

  • Amir F. Atiya

    (Department of Computer Engineering, Cairo University, Giza, Egypt)

Abstract

In this paper we propose a Bayesian forecasting approach for Holt's additive exponential smoothing method. Starting from the state space formulation, a formula for the forecast is derived and reduced to a two-dimensional integration that can be computed numerically in a straightforward way. In contrast to much of the work for exponential smoothing, this method produces the forecast density and, in addition, it considers the initial level and initial trend as part of the parameters to be evaluated. Another contribution of this paper is that we have derived a way to reduce the computation of the maximum likelihood parameter estimation procedure to that of evaluating a two-dimensional grid, rather than applying a five-variable optimization procedure. Simulation experiments confirm that both proposed methods give favorable performance compared to other approaches. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • Robert R. Andrawis & Amir F. Atiya, 2009. "A new Bayesian formulation for Holt's exponential smoothing," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(3), pages 218-234.
    • Handle: RePEc:jof:jforec:v:28:y:2009:i:3:p:218-234
    DOI: 10.1002/for.1094
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1002/for.1094
    File Function: Link to full text; subscription required
    Download Restriction: no
    File URL: https://libkey.io/10.1002/for.1094?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
    ---><---

    References listed on IDEAS

    as
    1. Hyndman, R.J. & Koehler, A.B. & Ord, J.K. & Snyder, R.D., 2001. "Prediction Intervals for Exponential Smoothing State Space Models," Monash Econometrics and Business Statistics Working Papers 11/01, Monash University, Department of Econometrics and Business Statistics.
    2. 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.
    3. Makridakis, Spyros & Hibon, Michele, 1991. "Exponential smoothing: The effect of initial values and loss functions on post-sample forecasting accuracy," International Journal of Forecasting, Elsevier, vol. 7(3), pages 317-330, November.
    4. Chris Chatfield, 1995. "Model Uncertainty, Data Mining and Statistical Inference," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 158(3), pages 419-444, May.
    5. Laurence Broze & Guy Melard, 1990. "Exponential smoothing: estimation by maximum likelihood," ULB Institutional Repository 2013/13716, ULB -- Universite Libre de Bruxelles.
    6. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.
    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. Forbes, C.S. & Snyder, R.D. & Shami, R.S., 2000. "Bayesian Exponential Smoothing," Monash Econometrics and Business Statistics Working Papers 7/00, Monash University, Department of Econometrics and Business Statistics.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Andrawis, Robert R. & Atiya, Amir F. & El-Shishiny, Hisham, 2011. "Forecast combinations of computational intelligence and linear models for the NN5 time series forecasting competition," International Journal of Forecasting, Elsevier, vol. 27(3), pages 672-688, July.
    2. Alysha M De Livera, 2010. "Automatic forecasting with a modified exponential smoothing state space framework," Monash Econometrics and Business Statistics Working Papers 10/10, Monash University, Department of Econometrics and Business Statistics.
    3. 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.
    4. Mirko Kremer & Brent Moritz & Enno Siemsen, 2011. "Demand Forecasting Behavior: System Neglect and Change Detection," Management Science, INFORMS, vol. 57(10), pages 1827-1843, October.

    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. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.
    2. 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.
    3. 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.
    4. 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.
    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. Kolassa, Stephan, 2011. "Combining exponential smoothing forecasts using Akaike weights," International Journal of Forecasting, Elsevier, vol. 27(2), pages 238-251, April.
    7. Fotios Petropoulos & Enno Siemsen, 2023. "Forecast Selection and Representativeness," Management Science, INFORMS, vol. 69(5), pages 2672-2690, May.
    8. Kolassa, Stephan, 2011. "Combining exponential smoothing forecasts using Akaike weights," International Journal of Forecasting, Elsevier, vol. 27(2), pages 238-251.
    9. 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.
    10. de Silva, Ashton J, 2010. "Forecasting Australian Macroeconomic variables, evaluating innovations state space approaches," MPRA Paper 27411, University Library of Munich, Germany.
    11. Alysha M De Livera, 2010. "Automatic forecasting with a modified exponential smoothing state space framework," Monash Econometrics and Business Statistics Working Papers 10/10, Monash University, Department of Econometrics and Business Statistics.
    12. 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).
    13. Meira, Erick & Cyrino Oliveira, Fernando Luiz & de Menezes, Lilian M., 2022. "Forecasting natural gas consumption using Bagging and modified regularization techniques," Energy Economics, Elsevier, vol. 106(C).
    14. Bergmeir, Christoph & Hyndman, Rob J. & Benítez, José M., 2016. "Bagging exponential smoothing methods using STL decomposition and Box–Cox transformation," International Journal of Forecasting, Elsevier, vol. 32(2), pages 303-312.
    15. Ralph D. Snyder & Anne B. Koehler, 2008. "A View of Damped Trend as Incorporating a Tracking Signal into a State Space Model," Monash Econometrics and Business Statistics Working Papers 7/08, Monash University, Department of Econometrics and Business Statistics.
    16. 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.
    17. 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.
    18. R Fildes & K Nikolopoulos & S F Crone & A A Syntetos, 2008. "Forecasting and operational research: a review," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1150-1172, September.
    19. 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.
    20. Makridakis, Spyros & Spiliotis, Evangelos & Assimakopoulos, Vassilios & Chen, Zhi & Gaba, Anil & Tsetlin, Ilia & Winkler, Robert L., 2022. "The M5 uncertainty competition: Results, findings and conclusions," International Journal of Forecasting, Elsevier, vol. 38(4), pages 1365-1385.

    More about this item

    Statistics

    Access and download statistics

    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:jof:jforec:v:28:y:2009:i:3:p:218-234. See general information about how to correct material in RePEc.

    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: Wiley-Blackwell Digital Licensing or Christopher F. Baum (email available below). General contact details of provider: http://www3.interscience.wiley.com/cgi-bin/jhome/2966 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.