Computational and Applied Mathematics

, Volume 36, Issue 4, pp 1545–1558 | Cite as

Weighted moving averaging revisited: an algebraic approach

  • Mantas Landauskas
  • Zenonas Navickas
  • Alfonsas Vainoras
  • Minvydas Ragulskis


An algebraic approach for the selection of weight coefficients for weighted moving averaging is proposed in this paper. The algebraic complexity of the sequence transformed by weighted moving averaging is set as a target criterion for the optimization problem of weight coefficients. A special computational setup is constructed in order to tackle the inevitable additive noise for real-world time series. Computational experiments prove that the proposed approach can outperform time series predictors based on classical moving averaging.


Moving average Time series prediction Weight coefficients 

Mathematics Subject Classification

37M10 11B37 37M99 



This work was supported by the Lithuanian Science Council under project No. MIP-078/2015.


  1. Chen KY (2011) Combining linear and nonlinear model in forecasting tourism demand. Exp Syst Appl 38(8):10368–10376Google Scholar
  2. Dong-xiao N, Hui-feng S, Desheng DW (2012) Short-term load forecasting using bayesian neural networks learned by hybrid monte carlo algorithm. Appl Soft Comput 12(6):1822–1827CrossRefGoogle Scholar
  3. Easton JF, Stephens CR, Angelova M (2014) Risk factors and prediction of very short term versus short/intermediate term post-stroke mortality: a data mining approach. Comput Biol Med 54:199–210CrossRefGoogle Scholar
  4. Firmino PRA, de Mattos Neto PS, Ferreira TA (2014) Correcting and combining time series forecasters. Neural Netw 50:1–11CrossRefzbMATHGoogle Scholar
  5. Holt CC (2004) Forecasting seasonals and trends by exponentially weighted moving averages. Int J Forecast 20(1):5–10CrossRefGoogle Scholar
  6. Hyndman RJ (2012) Time series data library. Accessed 16 Jan 2012
  7. Jia C, Wei L, Wang H, Yang J (2014) Study of track irregularity time series calibration and variation pattern at unit section. Comput Intell Neurosci 2014:14.
  8. Kurakin V (2001) Linear complexity of polinear sequences. Disctrete Math Appl 11(1):1–51CrossRefzbMATHMathSciNetGoogle Scholar
  9. Kurakin, VL, Kuzmin AVMAS, Nechavev AA (1995) Linear complexity of polinear sequences. J Math Sci 76:2793–2915Google Scholar
  10. Ma R, Hu SJ, Xu HH (2013) Very short-term wind speed prediction of a wind farm based on artificial neural network. Adv Mater Res Trans Tech Publ 608:677–682Google Scholar
  11. Manikandan MS, Soman K (2012) A novel method for detecting R-peaks in electrocardiogram (ECG) signal. Biomed Signal Process Control 7(2):118–128CrossRefGoogle Scholar
  12. Nan X, Li Q, Qiu D, Zhao Y, Guo X (2013) Short-term wind speed syntheses correcting forecasting model and its application. Int J Electric Power Energy Syst 49:264–268CrossRefGoogle Scholar
  13. Palivonaite R, Ragulskis M (2014) Short-term time series algebraic forecasting with internal smoothing. Neurocomputing 127:161–171CrossRefGoogle Scholar
  14. Park H, Elden L (2003) Matrix rank reduction for data analysis and feature extraction. Tech. rep., technical reportGoogle Scholar
  15. Ragulskis M, Lukoseviciute K, Navickas Z, Palivonaite R (2011) Short-term time series forecasting based on the identification of skeleton algebraic sequences. Neurocomputing 74(10):1735–1747CrossRefGoogle Scholar
  16. Sauer T, Yorke JA, Casdagli M (1991) J Stat Phys. Embedology 65(3–4):579–616Google Scholar
  17. Starzak ME (1989) Mathematical methods in chemistry and physics. Springer Science & Business Media, BerlinGoogle Scholar
  18. Trefethen LN (1999) Computation of pseudospectra. Acta Numerica 8:247–295CrossRefzbMATHMathSciNetGoogle Scholar
  19. Wang J, Hu Mm, Ge P, Ren Py, Zhao R (2014) A forecasting model for short term tourist arrival based on the empirical mode decomposition and support vector regression. In: Proceedings of 2013 4th international Asia conference on industrial engineering and management innovation (IEMI2013). Springer, Berlin, pp 1009–1021Google Scholar
  20. Weisstein EW (2015) Logistic map. From MathWorld–a wolfram web resource.
  21. Wright TG, Trefethen LN (2002) Pseudospectra of rectangular matrices. IMA J Numer Anal 22(4):501–519CrossRefzbMATHMathSciNetGoogle Scholar
  22. Zhang W, Wang J, Wang J, Zhao Z, Tian M (2013) Short-term wind speed forecasting based on a hybrid model. Appl Soft Comput 13(7):3225–3233CrossRefGoogle Scholar

Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2016

Authors and Affiliations

  • Mantas Landauskas
    • 1
  • Zenonas Navickas
    • 2
  • Alfonsas Vainoras
    • 3
  • Minvydas Ragulskis
    • 1
  1. 1.Research Group for Mathematical and Numerical Analysis of Dynamical SystemsKaunas University of TechnologyKaunasLithuania
  2. 2.Department of Applied MathematicsKaunas University of TechnologyKaunasLithuania
  3. 3.Sport InstituteLithuanian University of Health SciencesKaunasLithuania

Personalised recommendations