IDEAS home Printed from https://ideas.repec.org/p/msh/ebswps/2015-13.html
   My bibliography  Save this paper

STR: A Seasonal-Trend Decomposition Procedure Based on Regression

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp13-15.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Julius Shiskin, 1957. "Electronic Computers and Business Indicators," NBER Books, National Bureau of Economic Research, Inc, number juli57-1, March.
    2. 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.
    3. Alexander Dokumentov & Rob J Hyndman, 2014. "Low-dimensional decomposition, smoothing and forecasting of sparse functional data," Monash Econometrics and Business Statistics Working Papers 16/14, Monash University, Department of Econometrics and Business Statistics.
    4. 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).
    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.
    7. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737.
    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.
    10. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    11. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-227, June.
    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.
    13. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    14. 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.
    15. Julius Shiskin, 1957. "Electronic Computers and Business Indicators," The Journal of Business, University of Chicago Press, vol. 30, pages 219-219.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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. 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.
    4. Ollech, Daniel, 2018. "Seasonal adjustment of daily time series," Discussion Papers 41/2018, Deutsche Bundesbank.
    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. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    3. Otto-Sobotka, Fabian & Salvati, Nicola & Ranalli, Maria Giovanna & Kneib, Thomas, 2019. "Adaptive semiparametric M-quantile regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 116-129.
    4. Timothy K.M. Beatty & Erling Røed Larsen, 2005. "Using Engel curves to estimate bias in the Canadian CPI as a cost of living index," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(2), pages 482-499, May.
    5. Arthur Charpentier & Emmanuel Flachaire & Antoine Ly, 2017. "Econom\'etrie et Machine Learning," Papers 1708.06992, arXiv.org, revised Mar 2018.
    6. Hyunju Son & Youyi Fong, 2021. "Fast grid search and bootstrap‐based inference for continuous two‐phase polynomial regression models," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    7. Michael Wegener & Göran Kauermann, 2017. "Forecasting in nonlinear univariate time series using penalized splines," Statistical Papers, Springer, vol. 58(3), pages 557-576, September.
    8. Dlugosz, Stephan & Mammen, Enno & Wilke, Ralf A., 2017. "Generalized partially linear regression with misclassified data and an application to labour market transitions," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 145-159.
    9. Bernhard Baumgartner & Daniel Guhl & Thomas Kneib & Winfried J. Steiner, 2018. "Flexible estimation of time-varying effects for frequently purchased retail goods: a modeling approach based on household panel data," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(4), pages 837-873, October.
    10. Zi Ye & Giles Hooker & Stephen P. Ellner, 2021. "Generalized Single Index Models and Jensen Effects on Reproduction and Survival," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 492-512, September.
    11. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    12. Kalogridis, Ioannis & Van Aelst, Stefan, 2023. "Robust penalized estimators for functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    13. Krisztin, Tamás, 2018. "Semi-parametric spatial autoregressive models in freight generation modeling," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 121-143.
    14. Lauren N. Berry & Nathaniel E. Helwig, 2021. "Cross-Validation, Information Theory, or Maximum Likelihood? A Comparison of Tuning Methods for Penalized Splines," Stats, MDPI, vol. 4(3), pages 1-24, September.
    15. Nagler Thomas & Czado Claudia & Schellhase Christian, 2017. "Nonparametric estimation of simplified vine copula models: comparison of methods," Dependence Modeling, De Gruyter, vol. 5(1), pages 99-120, January.
    16. Yukun Zhang & Haocheng Li & Sarah Kozey Keadle & Charles E. Matthews & Raymond J. Carroll, 2019. "A Review of Statistical Analyses on Physical Activity Data Collected from Accelerometers," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(2), pages 465-476, July.
    17. Wei Huang & Oliver Linton & Zheng Zhang, 2021. "A Unified Framework for Specification Tests of Continuous Treatment Effect Models," Papers 2102.08063, arXiv.org, revised Sep 2021.
    18. Massimiliano Mazzanti & Antonio Musolesi, 2020. "Modeling Green Knowledge Production and Environmental Policies with Semiparametric Panel Data Regression models," SEEDS Working Papers 1420, SEEDS, Sustainability Environmental Economics and Dynamics Studies, revised Sep 2020.
    19. Basile, Roberto & Durbán, María & Mínguez, Román & María Montero, Jose & Mur, Jesús, 2014. "Modeling regional economic dynamics: Spatial dependence, spatial heterogeneity and nonlinearities," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 229-245.
    20. Morteza Amini & Mahdi Roozbeh & Nur Anisah Mohamed, 2024. "Separation of the Linear and Nonlinear Covariates in the Sparse Semi-Parametric Regression Model in the Presence of Outliers," Mathematics, MDPI, vol. 12(2), pages 1-17, January.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:msh:ebswps:2015-13. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Professor Xibin Zhang (email available below). General contact details of provider: https://edirc.repec.org/data/dxmonau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.