Skip to main content
Springer Nature Link
Log in

Structural Models: A Computational Look for Signal Extraction and Forecasting Seasonal Time Series

  • Original Research
  • Published:
SN Computer Science Aims and scope Submit manuscript

Abstract

Data analysis requires doing statistical programming which can be done at a simpler or more complex level. This article presents the main computational aspects for signal extraction, estimation and forecasting seasonal time series. From a structural model with covariates and different errors affecting the observations and the states, intelligent computational procedures are designed. First, the intelligent computational algorithms to obtain the main matrices of the system are derived; second, a general intelligent computational procedure and an algorithm that performs the Kalman filter and model estimation are also derived. Furthermore, the intelligent computational procedures and the structural model are evaluated using real seasonal time series, and the results demonstrate that the proposed method and model are very attractive and promising for model estimation, signal extraction and forecasting tasks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. For more details, see [34].

  2. See astsa: Applied Statistical Time Series Analysis. R package version 1.7.

References

  1. Alysha M, Hyndman RJ, Snyder RD. Forecasting time series with complex seasonal patterns using exponential smoothing. J Am Stat Assoc. 2011. https://doi.org/10.1198/jasa.2011.tm09771.

    Article  MathSciNet  MATH  Google Scholar 

  2. Arhipova I. The role of statistical methods in computer science and bioinformatics, 2006.

  3. Bauer A, Zufle M, Grohmann J, Schmitt N, Herbst N, Kounev S. An automated forecasting framework based on method recommendation for seasonal time series. Assoc Comput Mach. 2020;10(1145/3358960):3379123.

    Google Scholar 

  4. Box G, Cox D. An analysis of transformations. J R Stat Soc B. 1964;26(2):211–52.

    MATH  Google Scholar 

  5. Brockwell P, Davis R. Introduction to Time Series and Forecasting. 2nd ed. New York: Springer-Verlang; 2002.

    Book  Google Scholar 

  6. Bzdok D, Altman N, Krzywinski M. Statistics versus machine learning. Nat Methods. 2018. https://doi.org/10.1038/nmeth.4642.

    Article  Google Scholar 

  7. Calder M, et al. Computational modelling for decision-making: where, why, what, who and how.R. Soc Open Sci. 2018;5:172096. https://doi.org/10.1098/rsos.172096.

    Article  Google Scholar 

  8. Cankurt S, Subasi A. Developing tourism demand forecasting models using machine learning techniques with trend, seasonal, and cyclic components. Balkan J Electr Comput Eng. 2015;3(1):42–9.

    Google Scholar 

  9. Conway D, White JM. Machine learning for hackers. 1st ed. United States of America: O’Reilly; 2012.

    Google Scholar 

  10. Cordeiro C. Neves M. Forecasting with exponential smoothing methods and bootstrap: REVSTAT-Statistical Journal; 2011. p. 135–49.

  11. Cowpertwait PS, Metcalfe AV. Introductory Time Series with r. 2nd ed. New York: Springer; 2009.

    MATH  Google Scholar 

  12. Durstewitz D, Koppe G, Toutounji H. Computational models as statistical tools. Curr Opin Behav Sci. 2016. https://doi.org/10.1016/j.cobeha.2016.07.004.

    Article  Google Scholar 

  13. Dingli A, Fournier KS. Financial time series forecasting - a machine learning approach. Mach Learn Appl. 2017. https://doi.org/10.5121/mlaij.2017.4302.

    Article  Google Scholar 

  14. Dordonnat V, Koopman SJ, Ooms M, Dessertaine A, Collet J. An hourly periodic state space model for modelling French national electricity load. Int J Forecast. 2008;24:566–87.

    Article  Google Scholar 

  15. Durbin J, Koopman SJ. Time series analysis by state space methods. United Kingdom: Oxford University Press; 2011.

    MATH  Google Scholar 

  16. Evensen G. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J Geophys Res. 1994;99(10):143–62.

    Google Scholar 

  17. Guajardo JA, Weber R, Miranda J. A model updating strategy for predicting time series with seasonal patterns. Appl Soft Comput. 2010. https://doi.org/10.1016/j.asoc.2009.07.005.

    Article  Google Scholar 

  18. Gentle JE, Hardle W, Mori Y. How computational statistics became the backbone of modern data science. Economic Risk, Spandauer Strabe 1, D-10178 Berlin 2012; https://doi.org/10.1007/978-3-642-21551-3_1.

  19. Gob R, Lurz K, Pievatolo A. Electrical load forecasting by exponential smoothing with covariates. Appl Stoch Model Bus Ind. 2013;29:629–45.

    Article  MathSciNet  Google Scholar 

  20. Harvey AC, Koopman SJ. Forecasting hourly electricity demand using timevarying splines. J Am Stat Assoc. 1993;88:1228–366.

    Article  Google Scholar 

  21. Harvey AC. Forecasting. Structural time series models and the Kalman Filter. Cambridge: Cambridge University Press; 1989.

    Google Scholar 

  22. Hyndman RJ, Koehler AB, Snyder RD, Grose S. A state space framework for automatic forecasting using exponential smoothing methods. Int J Forecast. 2002;18:439–54.

    Article  Google Scholar 

  23. Hyndman RJ, Koehler AB, Ord JK, Snyder RD. Forecasting with Exponential Smoothing: The State Space Approach. Springer-Verlang 2008.

  24. Iniesta R, Stahl D, McGuffin P. Machine learning, statistical learning and the future of biological research in psychiatry. Psychol Med. 2016. https://doi.org/10.1017/S0033291716001367.

    Article  Google Scholar 

  25. Kitagawa G. Introduction to Time Series Modeling. Boca Raton: CRC Press; 2010.

    Book  Google Scholar 

  26. Koehler AB, Snyder RD, Ord JK, Beaumont A. A study of outliers in the exponential smoothing approach to forecasting. Int J Forecast. 2012;28:477–84.

    Article  Google Scholar 

  27. McKenzie ES, Gardner ES. Damped trend exponential smoothing: a modelling viewpoint. Int J Forecast. 2010;26:661–5.

    Article  Google Scholar 

  28. Mohamed A, Schwarz K. Adaptive Kalman filtering for INS/GPS. J Geod. 1999. https://doi.org/10.1007/s001900050236.

    Article  MATH  Google Scholar 

  29. Ord J, Koehler AB, Snyder RD. Estimation and prediction for a class of dynamic nonlinear statistical models. J Am Stat Assoc. 1997;92:1621–9.

    Article  Google Scholar 

  30. Ord J, Snyder RD, Koehler AB, Hyndman RJ, Leeds M. Time series forecasting: the case for the single source of error state space approach. Unpublished manuscript, Monash University 2005:2-33.

  31. Osman AF. Maxwell LK Exponential smoothing with regressors: estimation and initialization. Model Assist Stat Appl. 2015;10:253–63.

    Google Scholar 

  32. Pavlyshenko BM. Machine-learning models for sales time series. Forecasting. 2019. https://doi.org/10.3390/data4010015.

    Article  Google Scholar 

  33. Pedregal DJ, Young PC. Modulated cycles, an approach to modelling periodic components from rapidly sampled data. Int J Forecast. 2006;22:181–94.

    Article  Google Scholar 

  34. Puindi AC, Silva ME. Dynamic structural models with covariates for short-term forecasting of time series with complex seasonal patterns. J Appl Stat. 2020. https://doi.org/10.1080/02664763.2020.1748178.

    Article  Google Scholar 

  35. Rajula HSR, Verlato G, Manchia M, Antonucci N, Fanos V. Comparison of conventional statistical methods with machine learning in medicine: diagnosis, drug development, and Treatment. Medicina. 2020. https://doi.org/10.3390/medicina56090455.

    Article  Google Scholar 

  36. Rangapuram SS, Seeger M, Gasthaus J, Stella L, Wang Y, Januschowski T. Deep state space models for time series forecasting (NeurIPS), 32nd Conference on Neural Information Processing Systems. Canada: Montreal; 2018.

    Google Scholar 

  37. Ratnadip Adhikari R, Agrawal RK. Forecasting strong seasonal time series with artificial neural networks. J Scie Industr Res. 2012;71:657–66.

    Google Scholar 

  38. R Core Team: R. A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria 2017; software available at https://www.R-project.org.

  39. Razbash S, Hyndman, RJ. Forecasting functions for time series and linear models. cran.rproject.org, Package forecast 2018.

  40. Robert HS, Stoffer DS. Time series analysis and its applications: with R examples. 4th ed. New York: Springer; 2017.

    MATH  Google Scholar 

  41. Steven SH, Richard MG, Michael KT. Statistical modeling methods: challenges and strategies. Biostatist Epidemiol. 2020. https://doi.org/10.1080/24709360.2019.1618653.

    Article  Google Scholar 

  42. Taieb SB. Machine learning strategies for multi-step-ahead time series forecasting (Doutoral Thesis). Département d’Informatique: Université Libre de Bruxelles Belgium; 2014.

  43. Taylor JW, Buizza R. Using weather ensemble predictions in electricity demand forecasting. IEEE Trans. Power Syst. 2003;19:57–70.

    Google Scholar 

  44. Taylor JW. Short-term electricity demand forecasting using double seasonal exponential smoothing. J Operat Res Soc. 2003;54:799–805.

    Article  Google Scholar 

  45. Wang S. Exponential smoothing for forecasting and Bayesian validation of computer models, PhD thesis. Georgia Inst Technol. 2006;1(126):96.

    Google Scholar 

Download references

Acknowledgements

I would like to thank Professor Lukau Lwakiese for his comments, corrections and constructive suggestions.

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of 11 de Novembro, Cabinda, Angola

    António Casimiro Puindi

Authors
  1. António Casimiro Puindi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to António Casimiro Puindi.

Ethics declarations

Conflict of interest

The author declares that there is no conflict of interest.

Code Availability

All computational results of this work were obtained with the R software environment [38], available in https://github.com/antoniopuindi-code/ACPuindi-Rcode/tree/antoniopuindi-code-patch-2.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Puindi, A.C. Structural Models: A Computational Look for Signal Extraction and Forecasting Seasonal Time Series. SN COMPUT. SCI. 2, 96 (2021). https://doi.org/10.1007/s42979-021-00474-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s42979-021-00474-2

Keywords