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STR: A Seasonal-Trend Decomposition Procedure Based on Regression

Author

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  • Alexander Dokumentov
  • Rob J. Hyndman

Abstract

We propose new generic methods for decomposing seasonal data: STR (a Seasonal-Trend decomposition procedure based on Regression) and Robust STR. In some ways, STR is similar to Ridge Regression and Robust STR can be related to LASSO. Our new methods are much more general than any alternative time series decomposition methods. They allow for multiple seasonal and cyclic components, and multiple linear regressors with constant, flexible, seasonal and cyclic influence. Seasonal patterns (for both seasonal components and seasonal regressors) can be fractional and flexible over time; moreover they can be either strictly periodic or have a more complex topology. We also provide confidence intervals for the estimated components, and discuss how STR can be used for forecasting.

Suggested Citation

  • 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.
    • Handle: RePEc:msh:ebswps:2015-13
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp13-15.pdf
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    References listed on IDEAS

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    5. Rob J Hyndman & Shu Fan, 2008. "Density forecasting for long-term peak electricity demand," Monash Econometrics and Business Statistics Working Papers 6/08, Monash University, Department of Econometrics and Business Statistics.
    6. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 127-152, April.
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    8. Alexander Dokumentov & Rob J Hyndman, 2013. "Two-dimensional smoothing of mortality rates," Monash Econometrics and Business Statistics Working Papers 26/13, Monash University, Department of Econometrics and Business Statistics.
    9. 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.
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    12. McElroy Tucker S, 2010. "A Nonlinear Algorithm for Seasonal Adjustment in Multiplicative Component Decompositions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-23, September.
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    Cited by:

    1. Fang Han & Fei Zhao & Fuxing Li & Xiaoli Shi & Qiang Wei & Weimiao Li & Wei Wang, 2023. "Improvement of Monitoring Production Status of Iron and Steel Factories Based on Thermal Infrared Remote Sensing," Sustainability, MDPI, vol. 15(11), pages 1-17, May.
    2. Fataneh Dabaghi-Zarandi & Vahid Behjat & Michel Gauvin & Patrick Picher & Hassan Ezzaidi & Issouf Fofana, 2024. "Using Deep Learning to Detect Anomalies in On-Load Tap Changer Based on Vibro-Acoustic Signal Features," Energies, MDPI, vol. 17(7), pages 1-20, March.
    3. Ollech, Daniel, 2018. "Seasonal adjustment of daily time series," Discussion Papers 41/2018, Deutsche Bundesbank.
    4. Olivares, Kin G. & Challu, Cristian & Marcjasz, Grzegorz & Weron, Rafał & Dubrawski, Artur, 2023. "Neural basis expansion analysis with exogenous variables: Forecasting electricity prices with NBEATSx," International Journal of Forecasting, Elsevier, vol. 39(2), pages 884-900.
    5. Amirhossein Sohrabbeig & Omid Ardakanian & Petr Musilek, 2023. "Decompose and Conquer: Time Series Forecasting with Multiseasonal Trend Decomposition Using Loess," Forecasting, MDPI, vol. 5(4), pages 1-13, December.
    6. Seyma Gozuyilmaz & O. Erhun Kundakcioglu, 2021. "Mathematical optimization for time series decomposition," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 733-758, September.
    7. 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.

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    More about this item

    Keywords

    time series decomposition; seasonal data; Tikhonov regularisation; ridge regression; LASSO; STL; TBATS; X-12-ARIMA; BSM;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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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