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STR: Seasonal-Trend Decomposition Using Regression

Author

Listed:
  • Alexander Dokumentov

    (Let’s Forecast, Parkdale, Victoria 3195, Australia)

  • Rob J. Hyndman

    (Department of Econometrics & Business Statistics, Monash University, Clayton, Victoria 3800, Australia)

Abstract

We propose a new method for decomposing seasonal data: a seasonal-trend decomposition using regression (STR). Unlike other decomposition methods, STR allows for multiple seasonal and cyclic components, covariates, seasonal patterns that may have noninteger periods, and seasonality with complex topology. It can be used for time series with any regular time index, including hourly, daily, weekly, monthly, or quarterly data. It is competitive with existing methods when they exist and tackles many more decomposition problems than other methods allow. STR is based on a regularized optimization and so is somewhat related to ridge regression. Because it is based on a statistical model, we can easily compute confidence intervals for components, something that is not possible with most existing decomposition methods (such as seasonal-trend decomposition using Loess, X-12-ARIMA, SEATS-TRAMO, etc.). Our model is implemented in the R package stR , so it can be applied by anyone to their own data.

Suggested Citation

  • Alexander Dokumentov & Rob J. Hyndman, 2022. "STR: Seasonal-Trend Decomposition Using Regression," INFORMS Joural on Data Science, INFORMS, vol. 1(1), pages 50-62, April.
    • Handle: RePEc:inm:orijds:v:1:y:2022:i:1:p:50-62
    DOI: 10.1287/ijds.2021.0004
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    References listed on IDEAS

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    1. Julius Shiskin, 1957. "Electronic Computers and Business Indicators," NBER Books, National Bureau of Economic Research, Inc, number juli57-1, March.
    2. Commandeur, Jacques J. F. & Koopman, Siem Jan & Ooms, Marius, 2011. "Statistical Software for State Space Methods," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 41(i01).
    3. 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.
    4. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737.
    5. Montero-Manso, Pablo & Athanasopoulos, George & Hyndman, Rob J. & Talagala, Thiyanga S., 2020. "FFORMA: Feature-based forecast model averaging," International Journal of Forecasting, Elsevier, vol. 36(1), pages 86-92.
    6. Frederick R. Macaulay, 1931. "Appendices to "The Smoothing of Time Series"," NBER Chapters, in: The Smoothing of Time Series, pages 118-169, National Bureau of Economic Research, Inc.
    7. Frederick R. Macaulay, 1931. "The Smoothing of Economic Time Series, Curve Fitting and Graduation," NBER Chapters, in: The Smoothing of Time Series, pages 31-42, National Bureau of Economic Research, Inc.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    9. Frederick R. Macaulay, 1931. "The Smoothing of Time Series," NBER Books, National Bureau of Economic Research, Inc, number maca31-1, March.
    10. Thiyanga S Talagala & Rob J Hyndman & George Athanasopoulos, 2018. "Meta-learning how to forecast time series," Monash Econometrics and Business Statistics Working Papers 6/18, Monash University, Department of Econometrics and Business Statistics.
    11. Frederick R. Macaulay, 1931. "Introduction to "The Smoothing of Time Series"," NBER Chapters, in: The Smoothing of Time Series, pages 17-30, National Bureau of Economic Research, Inc.
    12. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    13. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
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