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Forecasting time series with multiple seasonal patterns

Author

Listed:
  • Gould, Phillip G.
  • Koehler, Anne B.
  • Ord, J. Keith
  • Snyder, Ralph D.
  • Hyndman, Rob J.
  • Vahid-Araghi, Farshid

Abstract

A new approach is proposed for forecasting a time series with multiple seasonal patterns. A state space model is developed for the series using the innovations approach which enables us to develop explicit models for both additive and multiplicative seasonality. Parameter estimates may be obtained using methods from exponential smoothing. The proposed model is used to examine hourly and daily patterns in hourly data for both utility loads and traffic flows. Our formulation provides a model for several existing seasonal methods and also provides new options, which result in superior forecasting performance over a range of prediction horizons. In particular, seasonal components can be updated more frequently than once during a seasonal cycle. The approach is likely to be useful in a wide range of applications involving both high and low frequency data, and it handles missing values in a straightforward manner.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:191:y:2008:i:1:p:207-222
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. repec:eee:ejores:v:264:y:2018:i:3:p:967-977 is not listed on IDEAS
    3. Reisen, Valdério A. & Zamprogno, Bartolomeu & Palma, Wilfredo & Arteche, Josu, 2014. "A semiparametric approach to estimate two seasonal fractional parameters in the SARFIMA model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 98(C), pages 1-17.
    4. Arora, Siddharth & Taylor, James W., 2016. "Forecasting electricity smart meter data using conditional kernel density estimation," Omega, Elsevier, vol. 59(PA), pages 47-59.
    5. Luis Fernando Melo Velandia & Daniel Parra Amado, 2014. "Efectos calendario sobre la producción industrial en Colombia," BORRADORES DE ECONOMIA 011241, BANCO DE LA REPÚBLICA.
    6. Shukur, Osamah Basheer & Lee, Muhammad Hisyam, 2015. "Daily wind speed forecasting through hybrid KF-ANN model based on ARIMA," Renewable Energy, Elsevier, vol. 76(C), pages 637-647.
    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. Andrew Harvey & Alessandra Luati, 2014. "Filtering With Heavy Tails," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1112-1122, September.
    9. 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.
    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. Shaun P Vahey & Elizabeth C Wakerly, 2013. "Moving towards probability forecasting," BIS Papers chapters,in: Bank for International Settlements (ed.), Globalisation and inflation dynamics in Asia and the Pacific, volume 70, pages 3-8 Bank for International Settlements.
    12. Lin, Yao-San & Li, Der-Chiang, 2010. "The Generalized-Trend-Diffusion modeling algorithm for small data sets in the early stages of manufacturing systems," European Journal of Operational Research, Elsevier, vol. 207(1), pages 121-130, November.
    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. Ramli, Azizul Azhar & Watada, Junzo & Pedrycz, Witold, 2011. "Real-time fuzzy regression analysis: A convex hull approach," European Journal of Operational Research, Elsevier, vol. 210(3), pages 606-617, May.
    15. repec:eee:phsmap:v:482:y:2017:i:c:p:42-55 is not listed on IDEAS
    16. 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.
    17. Carrizosa, Emilio & Olivares-Nadal, Alba V. & Ramírez-Cobo, Pepa, 2013. "Time series interpolation via global optimization of moments fitting," European Journal of Operational Research, Elsevier, vol. 230(1), pages 97-112.
    18. Aviral Kumar Tiwari & Claudiu T Albulescu & Phouphet Kyophilavong, 2014. "A comparison of different forecasting models of the international trade in India," Economics Bulletin, AccessEcon, vol. 34(1), pages 420-429.
    19. 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.
    20. 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.
    21. Mauro Bernardi & Lea Petrella, 2015. "Multiple seasonal cycles forecasting model: the Italian electricity demand," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(4), pages 671-695, November.
    22. Taylor, James W., 2008. "An evaluation of methods for very short-term load forecasting using minute-by-minute British data," International Journal of Forecasting, Elsevier, vol. 24(4), pages 645-658.
    23. Clements, A.E. & Hurn, A.S. & Li, Z., 2016. "Forecasting day-ahead electricity load using a multiple equation time series approach," European Journal of Operational Research, Elsevier, vol. 251(2), pages 522-530.

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