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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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    Cited by:

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    2. 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.
    3. 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.
    4. 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.
    5. Ollech, Daniel, 2018. "Seasonal adjustment of daily time series," Discussion Papers 41/2018, Deutsche Bundesbank.
    6. 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.
    7. 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.

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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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