Forecasting Trend-Seasonal Data Using Nonparametric Regression with Kernel and Fourier Series Approach

  • M. Fariz Fadillah MardiantoEmail author
  • Sri Haryatmi Kartiko
  • Herni Utami
Conference paper


Recently, forecasting time series data with trend and seasonal or trend-seasonal combinations with time series forecasting methods that are often used, are bound by assumptions that must be reached. If it does not reach the assumptions that exist, the forecasting process becomes longer. This study provides an alternative approach used for time series data forecasting that has trend-seasonal combination pattern using nonparametric regression. Some nonparametric regression approaches such as the kernel and the Fourier series can be done by considering the predictor as the time scale for a regular period. For the same data, using Nadaraya–Watson kernel approach and Fourier series in nonparametric regression gives different results. The result of prediction using nonparametric regression with the Fourier series approach is closer to the original data, when compared to the kernel approach. For each oscillation parameters inputted, nonparametric regression with the Fourier series approach always provides smaller MSE results than MSE in every bandwidth for Nadaraya–Watson kernel approach.


Nonparametric regression Kernel approach Fourier series approach Trend-seasonal data 


  1. 1.
    Bloomfield, P.: An Introduction Fourier Analysis for Time Series. Wiley, New York (2000)CrossRefGoogle Scholar
  2. 2.
    Bilodeau, M.: Fourier Smoother and Additive Models. Can. J. Stat. 3, 257–259 (1992). Scholar
  3. 3.
    Hardle, W.: Smoothing Techniques with Implementation in S. Springer, New York (1990)zbMATHGoogle Scholar
  4. 4.
    Eubank, R.L.: Spline Smoothing and Nonparametric Regression, 2nd edn. Marcel Dekker, New York (1999)zbMATHGoogle Scholar
  5. 5.
    Wahba, G.: Spline Model for Observational Data. SIAM XII, Philadelphia (1990)CrossRefGoogle Scholar
  6. 6.
    Green, P.J., Silverman, B.W.: Nonparametric Regression and Generalized Linear Models. Chapman and Hall, London (1994)CrossRefGoogle Scholar
  7. 7.
    Antoniadis, A., Bigot, J., Spatinas, T.: Wavelet estimators in nonparametric regression: a comparative simulation study. J. Stat. Softw. 6, 1–83 (2001). Scholar
  8. 8.
    Takezawa, K.: Introduction to Nonparametric Regression. Wiley, New Jearsy (2006)zbMATHGoogle Scholar
  9. 9.
    Li, F., Ionescu, C., Sminchisescu, C.: Random fourier approximations for skewed multiplicative histogram-kernels. Ann. Stat. 38(6), 3321–3351 (2013). Scholar
  10. 10.
    Pane, R., Budiantara, I.N., Zain, I., Otok, B.W.: Parametric and nonparametric estimators in fourier series semiparametric regression and their characteristics. Appl. Math. Sci. 8(102), 5053–5064 (2013). Scholar
  11. 11.
    Pujiastuti, C.E.: Fourier Series and Kernel in Nonparametric Regression. Gadjah Mada University, Yogyakarta (1996)Google Scholar
  12. 12.
    Harvey, A., Oryshchenko, V.: Kernel density estimation for time series data. Int. J. Forecast. 28(1), 3–14 (2012). ElsevierCrossRefGoogle Scholar
  13. 13.
    Box, G.E.P., Jenkins, G.M., Reinsel, G.C.: Time Series Analysis, Forecasting and Control, 3rd edn. Wiley, New York (1976)zbMATHGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • M. Fariz Fadillah Mardianto
    • 1
    • 2
    Email author
  • Sri Haryatmi Kartiko
    • 2
  • Herni Utami
    • 2
  1. 1.Department of MathematicsUniversity of AirlanggaSurabayaIndonesia
  2. 2.Department of MathematicsUniversity of Gadjah MadaYogyakartaIndonesia

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