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Time Series Prediction with Periodic Kernels

  • Marcin Michalak
Conference paper
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 95)

Abstract

This short article presents the new algorithm of time series prediction: PerKE. It implements the kernel regression for the time series directly without any data transformation. This method is based on the new type of kernel function – periodic kernel function – which two examples are also introduced in this paper. This new algorithm belongs to the group of semiparametric methods as it needs the initial step that separate the trend from the original time series.

Keywords

time series prediction regression kernel methods periodic kernel functions semiparametric methods 

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References

  1. 1.
    Abramson, I.S.: Arbitrariness of the pilot estimator in adaptive kernel methods. J. of Multivar. Anal. 12, 562–567 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Box, G.E.P., Jenkins, G.M.: Time series analysis. PWN, Warsaw (1983)Google Scholar
  3. 3.
    Epanechnikov, V.A.: Nonparametric Estimation of a Multivariate Probability Density. Theory of Probab. and its Appl. 14, 153–158 (1969)CrossRefGoogle Scholar
  4. 4.
    Fan, J., Gijbels, I.: Variable Bandwidth and Local Linear Regression Smoothers. Ann. of Stat. 20, 2008–2036 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Gasser, T., Kneip, A., Kohler, K.: A Flexible and Fast Method for Automatic Smoothing. J. of Am. Stat. Ass. 415, 643–652 (1991)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Gasser, T., Muller, H.G.: Estimating Regression Function and Their Derivatives by the Kernel Method. Scand. J. of Stat. 11, 171–185 (1984)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Hjort, N.L., Glad, I.K.: Nonparametric density estimation with a parametric start. Ann. of Stat. 23(3), 882–904 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Michalak, M.: Adaptive kernel approach to the time series prediction. Pattern Anal. and Appl. (2010), doi:10.1007/s10044-010-0189-3Google Scholar
  9. 9.
    Michalak, M.: Time series prediction using new adaptive kernel estimators. Adv. in Intell. and Soft Comput. 57, 229–236 (2009)Google Scholar
  10. 10.
    Nadaraya, E.A.: On estimating regression. Theory of Probab. and its Appl. 9, 141–142 (1964)CrossRefGoogle Scholar
  11. 11.
    Scott, D.W.: Multivariate Density Estimation. In: Theory, Practice and Visualization. Wiley & Sons, Chichester (1992)Google Scholar
  12. 12.
    Silverman, B.W.: Density Estimation for Statistics and Data Analysis. Chapman & Hall, Boca Raton (1986)zbMATHGoogle Scholar
  13. 13.
    Terrell, G.R.: The Maximal Smoothing Principle in Density Estimation. J. of Am. Stat. Ass. 410, 470–477 (1990)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Terrell, G.R., Scott, D.W.: Variable Kernel Density Estimation. Ann. of Stat. 20, 1236–1265 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Turlach, B.A.: Bandwidth Selection in Kernel Density Estimation: A Review. C.O.R.E. and Institut de Statistique, Universite Catholique de Louvain (1993)Google Scholar
  16. 16.
    Wand, M.P., Jones, M.C.: Kernel Smoothing. Chapman & Hall, Boca Raton (1995)zbMATHGoogle Scholar
  17. 17.
    Watson, G.S.: Smooth Regression Analysis. Sankhya - The Indian J. of Stat. 26, 359–372 (1964)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Marcin Michalak
    • 1
    • 2
  1. 1.Central Mining InstituteKatowicePoland
  2. 2.Silesian University of TechnologyGliwicePoland

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