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Forecasting Time-Series with Correlated Seasonality

Author

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

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 single source of error approach which enables us to develop explicit models for both additive and multiplicative seasonality. Parameter estimates may be obtained using methods adapted from general exponential smoothing, although the Kalman filter may also be used. 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. 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

  • Phillip Gould & Anne B. Koehler & Farshid Vahid-Araghi & Ralph D. Snyder & J. Keith Ord & Rob J. Hyndman, 2004. "Forecasting Time-Series with Correlated Seasonality," Monash Econometrics and Business Statistics Working Papers 28/04, Monash University, Department of Econometrics and Business Statistics, revised Oct 2005.
    • Handle: RePEc:msh:ebswps:2004-28
    as

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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2004/wp28-04.pdf
    File Function: Revised version, October 2005
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    References listed on IDEAS

    as
    1. [Reference to Proietti], Tommaso, 2000. "Comparing seasonal components for structural time series models," International Journal of Forecasting, Elsevier, vol. 16(2), pages 247-260.
    2. Ramanathan, Ramu & Engle, Robert & Granger, Clive W. J. & Vahid-Araghi, Farshid & Brace, Casey, 1997. "Shorte-run forecasts of electricity loads and peaks," International Journal of Forecasting, Elsevier, vol. 13(2), pages 161-174, June.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    4. Cottet R. & Smith M., 2003. "Bayesian Modeling and Forecasting of Intraday Electricity Load," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 839-849, January.
    5. 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.
    6. Ord, J.K. & Koehler, A. & Snyder, R.D., 1995. "Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models," Monash Econometrics and Business Statistics Working Papers 4/95, Monash University, Department of Econometrics and Business Statistics.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Masseran, Nurulkamal, 2016. "Modeling the fluctuations of wind speed data by considering their mean and volatility effects," Renewable and Sustainable Energy Reviews, Elsevier, vol. 54(C), pages 777-784.

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    More about this item

    Keywords

    Exponential smoothing; Holt-Winters; Seasonality; Structural time series model;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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