IDEAS home Printed from https://ideas.repec.org/a/eee/intfor/v26yi4p627-646.html
   My bibliography  Save this article

Exponentially weighted methods for forecasting intraday time series with multiple seasonal cycles

Author

Listed:
  • Taylor, James W.

Abstract

This paper introduces five new univariate exponentially weighted methods for forecasting intraday time series that contain both intraweek and intraday seasonal cycles. Applications of relevance include forecasting volumes of call centre arrivals, transportation, e-mail traffic and electricity loads. The first method that we develop extends an exponential smoothing formulation that has been used for daily sales data, and which involves smoothing the total weekly volume and its split across the periods of the week. Two new methods are proposed that use discount weighted regression (DWR). The first uses DWR to estimate the time-varying parameters of a model with trigonometric terms. The second introduces DWR splines. We also consider a time-varying spline that uses exponential smoothing. The final new method presented here involves the use of singular value decomposition followed by exponential smoothing. Empirical results are provided using a series of intraday call centre arrivals.

Suggested Citation

  • Taylor, James W., 2010. "Exponentially weighted methods for forecasting intraday time series with multiple seasonal cycles," International Journal of Forecasting, Elsevier, vol. 26(4), pages 627-646, October.
    • Handle: RePEc:eee:intfor:v:26:y::i:4:p:627-646
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0169-2070(10)00046-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tych, Wlodek & Pedregal, Diego J. & Young, Peter C. & Davies, John, 2002. "An unobserved component model for multi-rate forecasting of telephone call demand: the design of a forecasting support system," International Journal of Forecasting, Elsevier, vol. 18(4), pages 673-695.
    2. Alysha M De Livera & Rob J Hyndman, 2009. "Forecasting time series with complex seasonal patterns using exponential smoothing," Monash Econometrics and Business Statistics Working Papers 15/09, Monash University, Department of Econometrics and Business Statistics.
    3. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    4. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    5. Gould, Phillip G. & Koehler, Anne B. & Ord, J. Keith & Snyder, Ralph D. & Hyndman, Rob J. & Vahid-Araghi, Farshid, 2008. "Forecasting time series with multiple seasonal patterns," European Journal of Operational Research, Elsevier, vol. 191(1), pages 207-222, November.
    6. John Foster & Melvin J. Hinich & Phillip Wild, 2008. "Randomly Modulated Periodic Signals in Australias National Electricity Market," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 105-130.
    7. Weinberg, Jonathan & Brown, Lawrence D. & Stroud, Jonathan R., 2007. "Bayesian Forecasting of an Inhomogeneous Poisson Process With Applications to Call Center Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1185-1198, December.
    8. Taylor, James W. & de Menezes, Lilian M. & McSharry, Patrick E., 2006. "A comparison of univariate methods for forecasting electricity demand up to a day ahead," International Journal of Forecasting, Elsevier, vol. 22(1), pages 1-16.
    9. 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.
    10. Chris Brooks & Melvin J. Hinich, 2006. "Detecting intraday periodicities with application to high frequency exchange rates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 241-259, April.
    11. James W. Taylor, 2008. "A Comparison of Univariate Time Series Methods for Forecasting Intraday Arrivals at a Call Center," Management Science, INFORMS, vol. 54(2), pages 253-265, February.
    12. Haipeng Shen & Jianhua Z. Huang, 2005. "Analysis of call centre arrival data using singular value decomposition," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 21(3), pages 251-263, May.
    13. William Lam & Y. Tang & K. Chan & Mei-Lam Tam, 2006. "Short-term Hourly Traffic Forecasts using Hong Kong Annual Traffic Census," Transportation, Springer, vol. 33(3), pages 291-310, May.
    14. Haipeng Shen & Jianhua Z. Huang, 2008. "Interday Forecasting and Intraday Updating of Call Center Arrivals," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 391-410, July.
    15. J W Taylor, 2003. "Short-term electricity demand forecasting using double seasonal exponential smoothing," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 799-805, August.
    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. Md. Iftekharul Alam Efat & Petr Hajek & Mohammad Zoynul Abedin & Rahat Uddin Azad & Md. Al Jaber & Shuvra Aditya & Mohammad Kabir Hassan, 2024. "Deep-learning model using hybrid adaptive trend estimated series for modelling and forecasting sales," Annals of Operations Research, Springer, vol. 339(1), pages 297-328, August.
    2. Ayman A. Amin & Saeed A. Alghamdi, 2023. "Bayesian Identification Procedure for Triple Seasonal Autoregressive Models," Mathematics, MDPI, vol. 11(18), pages 1-13, September.
    3. Barrow, Devon & Kourentzes, Nikolaos, 2018. "The impact of special days in call arrivals forecasting: A neural network approach to modelling special days," European Journal of Operational Research, Elsevier, vol. 264(3), pages 967-977.
    4. Fullerton, Thomas M., Jr. & Mukhopadhyay, Somnath, 2013. "Border Region Bridge and Air Transport Predictability," MPRA Paper 59583, University Library of Munich, Germany, revised 11 Jul 2013.
    5. Luca Massidda & Marino Marrocu, 2018. "Smart Meter Forecasting from One Minute to One Year Horizons," Energies, MDPI, vol. 11(12), pages 1-16, December.
    6. Nystrup, Peter & Lindström, Erik & Møller, Jan K. & Madsen, Henrik, 2021. "Dimensionality reduction in forecasting with temporal hierarchies," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1127-1146.
    7. 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.
    8. Mauro Bernardi & Francesco Lisi, 2020. "Point and Interval Forecasting of Zonal Electricity Prices and Demand Using Heteroscedastic Models: The IPEX Case," Energies, MDPI, vol. 13(23), pages 1-34, November.
    9. Eichler, M. & Grothe, O. & Manner, H. & Türk, D.D.T., 2012. "Modeling spike occurrences in electricity spot prices for forecasting," Research Memorandum 029, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    10. Shao, Zhen & Chao, Fu & Yang, Shan-Lin & Zhou, Kai-Le, 2017. "A review of the decomposition methodology for extracting and identifying the fluctuation characteristics in electricity demand forecasting," Renewable and Sustainable Energy Reviews, Elsevier, vol. 75(C), pages 123-136.
    11. Barrow, Devon K., 2016. "Forecasting intraday call arrivals using the seasonal moving average method," Journal of Business Research, Elsevier, vol. 69(12), pages 6088-6096.
    12. Andrea Bastianin & Marzio Galeotti & Matteo Manera, 2011. "Forecast Evaluation in Call Centers: Combined Forecasts, Flexible Loss Functions and Economic Criteria," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1109, Universitá degli Studi di Milano.
    13. Lazos, Dimitris & Sproul, Alistair B. & Kay, Merlinde, 2014. "Optimisation of energy management in commercial buildings with weather forecasting inputs: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 39(C), pages 587-603.
    14. Taylor, James W. & Snyder, Ralph D., 2012. "Forecasting intraday time series with multiple seasonal cycles using parsimonious seasonal exponential smoothing," Omega, Elsevier, vol. 40(6), pages 748-757.
    15. Hugh Christensen & Simon Godsill & Richard E Turner, 2020. "Hidden Markov Models Applied To Intraday Momentum Trading With Side Information," Papers 2006.08307, arXiv.org.
    16. Sayar Karmakar & Marek Chudý & Wei Biao Wu, 2022. "Long‐term prediction intervals with many covariates," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 587-609, July.
    17. Sayar Karmakar & Marek Chudy & Wei Biao Wu, 2020. "Long-term prediction intervals with many covariates," Papers 2012.08223, arXiv.org, revised Sep 2021.
    18. James W. Taylor, 2012. "Density Forecasting of Intraday Call Center Arrivals Using Models Based on Exponential Smoothing," Management Science, INFORMS, vol. 58(3), pages 534-549, March.
    19. So, Mike K.P. & Chung, Ray S.W., 2014. "Dynamic seasonality in time series," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 212-226.
    20. Hill, Arthur V. & Zhang, Weiyong & Burch, Gerald F., 2015. "Forecasting the forecastability quotient for inventory management," International Journal of Forecasting, Elsevier, vol. 31(3), pages 651-663.
    21. Marcjasz, Grzegorz & Uniejewski, Bartosz & Weron, Rafał, 2020. "Probabilistic electricity price forecasting with NARX networks: Combine point or probabilistic forecasts?," International Journal of Forecasting, Elsevier, vol. 36(2), pages 466-479.
    22. Baek, Changryong & Davis, Richard A. & Pipiras, Vladas, 2017. "Sparse seasonal and periodic vector autoregressive modeling," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 103-126.
    23. Mun, Mak Kit & Chong, Choo Wei, 2018. "Forecasting Movie Demand Using Total and Split Exponential Smoothing," Jurnal Ekonomi Malaysia, Faculty of Economics and Business, Universiti Kebangsaan Malaysia, vol. 52(2), pages 81-94.
    24. Hsiao-Hui Lee & Edieal J. Pinker & Robert A. Shumsky, 2012. "Outsourcing a Two-Level Service Process," Management Science, INFORMS, vol. 58(8), pages 1569-1584, August.

    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. 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.
    2. Taylor, James W. & Snyder, Ralph D., 2012. "Forecasting intraday time series with multiple seasonal cycles using parsimonious seasonal exponential smoothing," Omega, Elsevier, vol. 40(6), pages 748-757.
    3. Barrow, Devon K., 2016. "Forecasting intraday call arrivals using the seasonal moving average method," Journal of Business Research, Elsevier, vol. 69(12), pages 6088-6096.
    4. Kim, Myung Suk, 2013. "Modeling special-day effects for forecasting intraday electricity demand," European Journal of Operational Research, Elsevier, vol. 230(1), pages 170-180.
    5. Barrow, Devon & Kourentzes, Nikolaos, 2018. "The impact of special days in call arrivals forecasting: A neural network approach to modelling special days," European Journal of Operational Research, Elsevier, vol. 264(3), pages 967-977.
    6. James W. Taylor, 2012. "Density Forecasting of Intraday Call Center Arrivals Using Models Based on Exponential Smoothing," Management Science, INFORMS, vol. 58(3), pages 534-549, March.
    7. Taylor, James W., 2010. "Triple seasonal methods for short-term electricity demand forecasting," European Journal of Operational Research, Elsevier, vol. 204(1), pages 139-152, July.
    8. Ibrahim, Rouba & Ye, Han & L’Ecuyer, Pierre & Shen, Haipeng, 2016. "Modeling and forecasting call center arrivals: A literature survey and a case study," International Journal of Forecasting, Elsevier, vol. 32(3), pages 865-874.
    9. Meade, Nigel & Islam, Towhidul, 2015. "Forecasting in telecommunications and ICT—A review," International Journal of Forecasting, Elsevier, vol. 31(4), pages 1105-1126.
    10. Theresa Maria Rausch & Tobias Albrecht & Daniel Baier, 2022. "Beyond the beaten paths of forecasting call center arrivals: on the use of dynamic harmonic regression with predictor variables," Journal of Business Economics, Springer, vol. 92(4), pages 675-706, May.
    11. Andrea Bastianin & Marzio Galeotti & Matteo Manera, 2019. "Statistical and economic evaluation of time series models for forecasting arrivals at call centers," Empirical Economics, Springer, vol. 57(3), pages 923-955, September.
    12. Kinshuk Jerath & Anuj Kumar & Serguei Netessine, 2015. "An Information Stock Model of Customer Behavior in Multichannel Customer Support Services," Manufacturing & Service Operations Management, INFORMS, vol. 17(3), pages 368-383, July.
    13. Smirnov, Dmitry & Huchzermeier, Arnd, 2020. "Analytics for labor planning in systems with load-dependent service times," European Journal of Operational Research, Elsevier, vol. 287(2), pages 668-681.
    14. Chethana Dharmawardane & Ville Sillanpää & Jan Holmström, 2021. "High-frequency forecasting for grocery point-of-sales: intervention in practice and theoretical implications for operational design," Operations Management Research, Springer, vol. 14(1), pages 38-60, June.
    15. Webel, Karsten, 2022. "A review of some recent developments in the modelling and seasonal adjustment of infra-monthly time series," Discussion Papers 31/2022, Deutsche Bundesbank.
    16. Itai Gurvich & James Luedtke & Tolga Tezcan, 2010. "Staffing Call Centers with Uncertain Demand Forecasts: A Chance-Constrained Optimization Approach," Management Science, INFORMS, vol. 56(7), pages 1093-1115, July.
    17. Albrecht, Tobias & Rausch, Theresa Maria & Derra, Nicholas Daniel, 2021. "Call me maybe: Methods and practical implementation of artificial intelligence in call center arrivals’ forecasting," Journal of Business Research, Elsevier, vol. 123(C), pages 267-278.
    18. Tevfik Aktekin & Refik Soyer, 2011. "Call center arrival modeling: A Bayesian state‐space approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(1), pages 28-42, February.
    19. Haipeng Shen & Jianhua Z. Huang, 2008. "Interday Forecasting and Intraday Updating of Call Center Arrivals," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 391-410, July.
    20. Taylor, James W., 2008. "Exponentially weighted information criteria for selecting among forecasting models," International Journal of Forecasting, Elsevier, vol. 24(3), pages 513-524.

    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:eee:intfor:v:26:y::i:4:p:627-646. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijforecast .

    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.