Gold Price Fluctuation Forecasting Based on Newton and Lagrange Polynomial Interpolation
Abstract
Gold is a highly valuable commodity and an investment opportunity for many people. However, there are often significant fluctuations in gold prices that affect investment decisions. Various mathematical forecasting methods have been developed to anticipate gold price fluctuations. This study uses historical daily data of gold prices during January-May 2023. The method used in this study is the Newton and Lagrange polynomial interpolation method with several orders to analyze data and forecast gold price fluctuations. The purpose of this study is to compare the performance and accuracy of the order levels of the Newton and Lagrange polynomial interpolation forecasting models. In this study, the test data points and orders are selected so that a range is formed that matches the amount of data available. The test orders used in this study include orders 2, 3, 5, 6, and 10. This study found that the 2nd order polynomial interpolation method is more effective and accurate in forecasting gold price fluctuations compared to the higher orders tested. This is indicated by the results of the calculation of MAE, RMSE, and MAPE values in 2nd order polynomial interpolation which are smaller than in 3rd, 5th, 6th, and 10th order polynomial interpolation. This suggests that a polynomial of 2nd order has been able to model and forecast gold price fluctuations well. However, it is important to remember that these conclusions are based on the data and methods used in this study. Variability in forecasting results can occur depending on the quality of the data, the time period used, and the interpolation method applied, among others. Therefore, further research and wider testing needs to be conducted to validate these conclusions.
References
Menggunakan Model ARIMA. Jurnal Aplikasi Statistika & Komputasi Statistik, 12(1):71–84. https://doi.org/10.34123/jurnalasks.
v12i1.264.
Astuti, L. W., Sudarwanto, and Ambarwati, L. (2018). Perbandingan Metode Lagrange dan Metode Newton pada Interpolasi Polinomial dalam Mengestimasi Harga Saham. JMT (Jurnal Matematika dan Terapan, 2(1):25–35.
Aulia, R., Sazlin, R. A., Ismayani, L., Sukiman, M., Perwira Negara, H. R., and Ayu Kurniawati, K. R. (2020). Implementasi
Interpolasi Newton Gregory pada Model Matematika Penyebaran Virus Corona di Indonesia.
Haris, M. A. (2020). Peramalan Harga Emas Dengan Model Generalized Autoregressive Conditional Heteroscedasticity (Garch).
Jurnal Saintika Unpam : Jurnal Sains dan Matematika Unpam, 3(1):19. https://doi.org/10.32493/jsmu.v3i1.5263.
Hariwijaya, M. R. I., Furqon, M. T., and Dewi, C. (2020). Prediksi Harga Emas Dengan Menggunakan Metode Average-Based Fuzzy
Time Series. Jurnal Pengembangan Teknologi Informasi dan Ilmu Komputer, 4(4):1258–1264.
Hendrian, J., Suparti, S., and Prahutama, A. (2021). Pemodelan Harga Emas Dunia Menggunakan Metode Nonparametrik Polinomial
Lokal Dilengkapi GUI R. Jurnal Gaussian, 10(4):605–616. https://doi.org/10.14710/j.gauss.10.4.605-616.
Hurit, R. U. and Nanga, M. Y. (2022). Penerapan Metode Interpolasi Lagrange dalam Memprediksi Jumlah Penduduk Provinsi Nusa
Tenggara Timur. Math Educa Journal, 6(1):57–62.
Lamabelawa, M. I. J. (2019). Perbandingan Interpolasi Dan Ekstrapolasi Newton. High Education of Organization Archive Quality:
Jurnal Teknologi Informasi, 10(2):73–80. https://doi.org/10.52972/hoaq.vol10no2.p73-80.
Mahena, Y., Rusli, M., and Winarso, E. (2015). Prediksi Harga Emas Dunia Sebagai Pendukung Keputusan Investasi Saham Emas
Menggunakan Teknik Data Mining. Kalbiscentia Jurnal Sains dan Teknologi, 2(1):36–51.
Muhammad, D. (2011). Penggunaan Metode Newton dan Lagrange pada Interpolasi Polinom Pergerakan Harga Saham : Studi Kasus
Saham PT Adaro Energi Tbk. Technical report.
Muhammad Julian, Lukita Ambarwati, and Yudi Mahatma (2022). Penentuan Derajat Optimum Interpolasi pada Metode Lagrange
dan Metode Newton Gregory dalam Mengestimasi Kasus Pasien Sembuh dari Covid-19 di Indonesia. JMT : Jurnal Matematika
dan Terapan, 4(1):11–18. https://doi.org/10.21009/jmt.4.1.2.
Negara, H. R. P., Ibrahim, M., and Kurniawati, K. R. A. (2020). Mathematical Model of Growth in The Number of Students in NTB
Using Newton-Gregory Polynomial Method. Jurnal Varian, 4(1):43–50. https://doi.org/10.30812/varian.v4i1.850.
Nugroho, B. P. (2018). Implementasi Sistem Untuk Prediksi Harga Emas. Jurnal SAINTEKOM, 8(2):90–104. https://doi.org/10.
33020/saintekom.v8i2.56.
Pangruruk, F. A. and Barus, S. P. (2016). Prediksi Harga Saham Menggunakan Metode Interpolasi Polinom Lagrange. In Prosiding
Seminar Nasional Matematika dan Pendidikan Matematika, pages 1–8.
Pangruruk, F. A. and Barus, S. P. (2018a). Prediksi Harga Saham dengan Interpolasi Polinom Newton Gregory Maju. In Program
Studi Pendidikan Matematika FKIP UMS, pages 644–650.
Pangruruk, F. A. and Barus, S. P. (2018b). Prediksi Harga Saham Menggunakan Metode Interpolasi Polinom Newton Gregory
Mundur. In Prosiding SEMADIK, number April, pages 24–29.
Pangruruk, F. A., Barus, S. P., and Siregar, B. (2020). Peramalan Harga Saham Tutup Dengan Metode Interpolasi Polinom Lagrange.
In Prosiding Seminar Nasional Variansi, pages 118–126.
Pragna, C., Purra, B., Viharika, A., Roshni, G., and Prajna, P. B. (2022). Gold Price Prediction Using Machine Learning Techniques.
International Research Journal of Modernization in Engineering Technology and Science (IRJMETS), 4(05):117–120.
Pratama, R., Sianipar, R. H., and Wiryajati, I. K. (2014). Pengaplikasian Metode Interpolasi dan Ekstrapolasi Lagrange, Chebyshev,
dan Spline Kubik untuk Memprediksi Angka Pengangguran di Indonesia. Dielektrika, 1(2):116–121.
Pratiwi, G. A., Jaya, A. I., and Ratianingsih, R. (2017). Aplikasi Metode Polinom Newton Gregory Maju dan Polinom Newton
Gregory Mundur dalam Memprediksi Banyaknya Penduduk Sulawesi Tengah. Jurnal Ilmiah Matematika dan Terapan (JIMT),
14(2):152–158.
Radhamani, V., Manju, D., Bobby, P. M., Javagar, M., Nivetha, V., and Rinubha, P. (2022). Gold Price Prediction Using ML
Algorithms. YMER, 21(7):183–192.
Rakhmawati, D. and Nurhalim, M. (2021). Prediksi Harga Emas Berjangka di Masa Pandemi Covid-19 Menggunakan Model Tren
Deterministik. Akuntabel, 18(1):146–152. https://doi.org/10.30872/jakt.v18i1.9145.
Sihombing, S. C. (2019). Prediksi Hasil Produksi Pertanian Kelapa Sawit di Provinsi Riau dengan Pendekatan Interpolasi Newton
Gregory Forward (NGF). In Prosiding Seminar Nasional II Hasil Litbangyasa Industri, pages 63–70.
Siregar, R. R. A., Djatna, T., Manullang, S. S. M. P., and Saputra, I. (2021). Double Exponential Smoothing Berimputasi LOCF Dan
Linear Interpolation dalam Akurasi Peramalan Harga Harian Emas. KILAT, 10(1):208–222. https://doi.org/10.33322/kilat.v10i1.
1200.Sravani, M., Abhilash, C., Divya, T., Vasthav, C., and Priyanka, D. (2021). Gold Price Prediction. International Journal of Creative
Research Thoughts (IJCRT), 9(6):745–747.
Sunyanti. and Mukhaiyar, U. (2019). Gold Price Prediction Using ARIMA Time Series Model Approach. Procuratio: Jurnal Ilmiah
Manajemen, 7(4):379–390.
Suryana, Y. and Sen, T. W. (2021). The Prediction of Gold Price Movement by Comparing Naive Bayes, Support Vector Machine,
and K-NN. Jurnal Informatika dan Sains (JISA), 4(2):112–120. https://doi.org/10.31326/jisa.v4i2.922.
Tripurana, N., Kar, B., Chakravarty, S., Paikaray, B. K., and Satpathy, S. (2022). Gold Price Prediction Using Machine Learning
Techniques. In CEUR Workshop Proceedings, pages 274–281. https://doi.org/10.22214/ijraset.2021.35831.
ul Sami, I. and Junero, K. N. (2017). Predicting Future Gold Rates using Machine Learning Approach. International Journal of
Advanced Computer Science and Applications (IJACSA), 8(12):92–99. https://doi.org/10.14569/ijacsa.2017.081213.
This work is licensed under a Creative Commons Attribution 4.0 International License.