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

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  • 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.

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  • 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
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    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.
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    3. 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.
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      • 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.
    7. 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.
    8. 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).
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Hugh Christensen & Simon Godsill & Richard E Turner, 2020. "Hidden Markov Models Applied To Intraday Momentum Trading With Side Information," Papers 2006.08307, arXiv.org.
    15. 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.
    16. Sayar Karmakar & Marek Chudy & Wei Biao Wu, 2020. "Long-term prediction intervals with many covariates," Papers 2012.08223, arXiv.org, revised Sep 2021.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.

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