Regresi Nonparametrik dengan Pendekatan Deret Fourier pada Data Debit Air Sungai Citarum

  • Intaniah Ratna Nur Wisisono Universitas Padjadjaran
  • Ade Irma Nurwahidah Universitas Padjadjaran
  • Yudhie Andriyana Universitas Padjadjaran
Keywords: Fourier, ARIMA, River discharge, Nonparametric

Abstract

River discharge is one of the factors that affect the occurrence of floods. It varies over time and hence we need to predict the flood risk. Since the plot of the data changes periodically showing a sines and cosines pattern, a nonparametric technique using Fourier series approach may be interesting to be applied. Fourier series can be estimated using OLS (Ordinary Least Square). In a Fourier series, nonparametric regression the level of subtlety of its function is determined by their bandwidth (K). Optimal bandwidth determined using the GCV (Generalized Cross Validation) method. From the calculation results, we have optimal bandwidth which is equal to 16 with R2 is 0.7295 which means that 72.95% of the total variance in the river discharge variable can be explained by the Fourier series nonparametric regression model. Comparing to a classical time series technique, ARIMA Box Jenkins, we obtained ARIMA (1,0,0) with RMSE 83.10 while using Fourier series approach generate a smaller RMSE 50.51.

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References

Asrini, Luh Juni. “Regresi Parametrik Deret Fourier”, Prosiding Seminar Nasional FMIPA Universitas Negeri Surabaya, (2012) 77-80, 24 November, Surabaya.

Bilodeau, M. “Fourier Smoother and Additive Models”, The Canadian Journal of Statistics, 3, (1992) 257-259.

Eubank, R., Nonparametric Regression and Spline Smoothing. New York: Marcel Dekker. (1999).

Hardle, Wolfgang. 1994. Applied Nonparametric Regression. Springer-Verlag. Berlin. (1994).

Mulyana. Pemodelan Debit Air Sungai Studi Kasus DAS Cikapundung. Makalah, disampaikan pada Lokakarya Sistem Informasi Pengelolaan DAS: Inisiatif Pengembangan Infrastruktur Data. IPB. (2007). 5 September, Bogor.

Nurjanah, Fatmawati dkk. Model Regresi Nonparametrik Dengan Pendekatan Deret Fourier Pada Pola Data Curah Hujan di Kota Semarang. Universitas Muhammadiyah Semarang. Semarang. (2015).

Pankratz, A. Forecasting with Univariate Box-Jenkins Models: Concepts and Cases. John Wiley and Sons, New York. (1983).

Prahutama, Alan. Model Regresi Nonparametrik Dengan Pendekatan Deret Fourier Pada Kasus Tingkat Pengangguran Terbuka di Jawa Timur. Prosiding Seminar Nasional Statistika. Universitas Diponegoro. (2013). Semarang.

Tripena, A. Tesis. Estimator Deret Fourier dalam Regresi Nonparametrik, ITS,

Surabaya. 2007.

Wu, H. dan Zhang, J.T. Nonparametric Regression Methods for Longitudinal Data Analysis, A John-Wiley and Sons Inc. Publication, New Jersey. (2006).

Ulinnuha, Nurissaidah dan Farida, Yuniar “Prediksi Cuaca Kota Surabaya Menggunakan Autoregressive Integrated Moving Average (ARIMA) Box Jenkins dan Kalman Filter”, Jurnal Matematika MANTIK, vol. 4, no. 1, hal. 59-67, Mei 2018

Published
2018-10-31
How to Cite
Nur Wisisono, I., Nurwahidah, A., & Andriyana, Y. (2018). Regresi Nonparametrik dengan Pendekatan Deret Fourier pada Data Debit Air Sungai Citarum. Jurnal Matematika "MANTIK", 4(2), 75-82. https://doi.org/10.15642/mantik.2018.4.2.75-82
Section
Articles