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Forecasting time series with complex seasonal patterns using exponential smoothing

Author

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  • Alysha M De Livera
  • Rob J Hyndman

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Abstract

A new innovations state space modeling framework, incorporating Box-Cox transformations, Fourier series with time varying coefficients and ARMA error correction, is introduced for forecasting complex seasonal time series that cannot be handled using existing forecasting models. Such complex time series include time series with multiple seasonal periods, high frequency seasonality, non-integer seasonality and dual-calendar effects. Our new modelling framework provides an alternative to existing exponential smoothing models, and is shown to have many advantages. The methods for initialization and estimation, including likelihood evaluation, are presented, and analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors are derived, leading to a simple, comprehensible approach to forecasting complex seasonal time series. Our trigonometric formulation is also presented as a means of decomposing complex seasonal time series, which cannot be decomposed using any of the existing decomposition methods. The approach is useful in a broad range of applications, and we illustrate its versatility in three empirical studies where it demonstrates excellent forecasting performance over a range of prediction horizons. In addition, we show that our trigonometric decomposition leads to the identification and extraction of seasonal components, which are otherwise not apparent in the time series plot itself.

Suggested Citation

  • 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.
  • Handle: RePEc:msh:ebswps:2009-15
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2009/wp15-09.pdf
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    Citations

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    Cited by:

    1. Alexander Dokumentov & Rob J. Hyndman, 2015. "STR: A Seasonal-Trend Decomposition Procedure Based on Regression," Monash Econometrics and Business Statistics Working Papers 13/15, Monash University, Department of Econometrics and Business Statistics.
    2. Kolassa, Stephan, 2011. "Combining exponential smoothing forecasts using Akaike weights," International Journal of Forecasting, Elsevier, vol. 27(2), pages 238-251, April.
    3. Luis Fernando Melo Velandia & Daniel Parra Amado, 2014. "Efectos calendario sobre la producción industrial en Colombia," BORRADORES DE ECONOMIA 011241, BANCO DE LA REPÚBLICA.
    4. Hossein Hassani & Emmanuel Sirimal Silva & Rangan Gupta & Mawuli K. Segnon, 2015. "Forecasting the price of gold," Applied Economics, Taylor & Francis Journals, vol. 47(39), pages 4141-4152, August.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Alan J Auerbach & Yuriy Gorodnichenko, 2016. "Effects of Fiscal Shocks in a Globalized World," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 64(1), pages 177-215, May.
    10. Davinson Stev Abril Salcedo & Luis Fernando Melo Velandia & Daniel Parra Amado, 2015. "Heterogeneidad de los Índices de Producción Sectoriales de la Industria Colombiana," BORRADORES DE ECONOMIA 012973, BANCO DE LA REPÚBLICA.
    11. 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.
    12. 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.
    13. Irma Hindrayanto & Jan Jacobs & Denise Osborn, 2014. "On trend-cycle-seasonal interactions," DNB Working Papers 417, Netherlands Central Bank, Research Department.
    14. Kolassa, Stephan, 2011. "Combining exponential smoothing forecasts using Akaike weights," International Journal of Forecasting, Elsevier, vol. 27(2), pages 238-251.

    More about this item

    Keywords

    Exponential smoothing; Fourier series; prediction intervals; seasonality; state space models; time series decomposition;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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