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April 12, 2025
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June 26, 2025
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June 30, 2025
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Abstract
Pulau Sumatra merupakan salah satu wilayah di Indonesia dengan tingkat risiko gempa bumi yang tinggi akibat jalur subduksi dan keberadaan sesar aktif. Penelitian ini bertujuan untuk memodelkan dan meramalkan magnitudo tertinggi gempa bumi tahunan di Pulau Sumatra menggunakan metode Autoregressive Integrated Moving Average (ARIMA) dan Seasonal Autoregressive Integrated Moving Average (SARIMA). Data yang digunakan adalah magnitudo tahunan dari tahun 1900 hingga 2023. Sebelum pemodelan, dilakukan uji stasioneritas data melalui transformasi Box-Cox untuk varians dan uji Augmented Dickey-Fuller (ADF) untuk rataan. Setelah proses differencing, data dinyatakan stasioner terhadap rataan. Identifikasi model awal dilakukan dengan analisis plot ACF dan PACF, diikuti dengan seleksi model berdasarkan signifikansi parameter. Evaluasi model menggunakan kriteria AIC, BIC, MAE, RMSE, dan MAPE. Hasil analisis menunjukkan bahwa model SARIMA (1,1,1) (1,1,0)24 memiliki performa terbaik berdasarkan nilai AIC, BIC, MAE, dan MAPE. Namun, dalam tahap peramalan data testing, model ARIMA (2,1,2) menunjukkan hasil prediksi yang lebih mendekati nilai aktual. Penelitian ini menunjukkan bahwa kombinasi penggunaan ARIMA dan SARIMA dapat membantu dalam memodelkan kejadian gempa bumi di Sumatra, dengan pemilihan model terbaik disesuaikan berdasarkan tujuan peramalan.
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Copyright (c) 2025 Muhammad A. Firmansyah, Cinta R. Oktarina
This work is licensed under a Creative Commons Attribution 4.0 International License.
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Firmansyah, M. A., & Oktarina, C. R. (2025). Kinerja Peramalan Autoregressive Integrated Moving Average dan Seasonal Autoregressive Integrated Moving Average dalam Memprediksi Kejadian Gempa Bumi Sumatra. Diophantine Journal of Mathematics and Its Applications, 4(1), 1–16. https://doi.org/10.33369/diophantine.v4i1.41099
References
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[1] R. Metrikasari and A. Choiruddin, “Pemodelan Risiko Gempa Bumi di Pulau Sumatera Menggunakan Model Inhomogeneous Neyman-Scott Cox Process,” J. Sains dan Seni ITS, vol. 9, no. 2, 2021, doi: 10.12962/j23373520.v9i2.52318.
[2] Sunarjo, M. T. Gunawan, and S. Pribadi, Gempabumi Edisi Populer, II. Jakarta: Badan Meteorologi Klimatologi dan Geofisika, 2012.
[3] Kementrian ESDM, Pengenalan Gempa Bumi. Jakarta: Kementrian ESDM, 2013.
[4] Badan Meteorologi Klimatologi dan Geofisika (BMKG), “Rencana Strategis BMKG 2020-2024,” pp. 10–11; 60–63, 2020, [Online]. Available: https://www.bmkg.go.id/profil/?p=rencana-strategis
[5] W. Asnita, D. Sugiyanto, and I. Rusydy, “Kajian Statistik Seismisitas Kawasan Sumatera,” J. Nat., vol. 16, no. 2, 2016.
[6] G. E. P. Box and G. M. Jenkins, Time Series Analysis Forecasting and Control, Revised. Oakland, California: Holden Day, 1976. doi: 10.2307/2284112.
[7] H. H. M. Hatta, F. M. Daud, and N. Mohamad, “An Application of Time Series ARIMA Forecasting Model for Predicting the Ringgit Malaysia-Dollar Exchange Rate,” J. Data Anal., vol. 1, no. 1, pp. 42–48, 2018, doi: 10.24815/jda.v1i1.11884.
[8] H. Nie, G. Liu, X. Liu, and Y. Wang, “Hybrid of ARIMA and SVMs for short-term load forecasting,” in Energy Procedia, 2012, pp. 1455–1460. doi: 10.1016/j.egypro.2012.01.229.
[9] C. Chen, R. A. Davis, and P. J. Brockwell, “Order determination for multivariate autoregressive processes using resampling methods,” J. Multivar. Anal., vol. 57, no. 2, pp. 175–190, 1996, doi: 10.1006/jmva.1996.0028.
[10] J. E. Hanke and D. Wichern, Business Forecasting (Ninth Edition), vol. 5, no. 1. 2014. [Online]. Available: https://ejournal.poltektegal.ac.id/index.php/siklus/article/view/298%0Ahttp://repositorio.unan.edu.ni/2986/1/5624.pdf%0Ahttp://dx.doi.org/10.1016/j.jana.2015.10.005%0Ahttp://www.biomedcentral.com/1471-2458/12/58%0Ahttp://ovidsp.ovid.com/ovidweb.cgi?T=JS&P
[11] D. N. Gujarati and D. J. Porter, Dasar-Dasar Ekonometrika, 5th ed. Jakarta: Salemba Empat, 2013.
[12] A. F. Salaam, W. Somayasa, and M. K. Djafar, “Estimasi Parameter Genetik Gamma Untuk Sampel Tersensor Tipe I dan Tipe II,” J. Mat. Komputasi dan Stat., vol. 3, no. 1, pp. 238–244, 2023, [Online]. Available: http://jmks.uho.ac.id/index.php/JMKS
[13] I. Ghozali, Aplikasi Analisis Multivariete Dengan Program IBM SPSS 23, 8th ed. Semarang: Badan Penerbit Universitas Diponegoro, 2016.
[14] G. E. P. Box and D. A. Pierce, “Distribution of residual autocorrelations in autoregressive-integrated moving average time series models,” J. Am. Stat. Assoc., vol. 65, no. 332, pp. 1509–1526, 1970, doi: 10.1080/01621459.1970.10481180.
[15] A. Hidayat, “Uji Normalitas dan Metode Perhitungan (Penjelasan Lengkap),” Statiskian.com. Accessed: Jun. 04, 2024. [Online]. Available: https://www.statistikian.com/2013/01/uji-normalitas.html
[16] J. Barkus and C. Yavorsky, Understanding and using advanced statistics. London: Sage Publications, Inc, 2006.
[17] R. J. Hyndman and G. Athanasopoulos, Forecasting: Principles and Practice, 2nd ed. 2018. [Online]. Available: https://otexts.com/fpp2/arima-forecasting.html
References
[1] R. Metrikasari and A. Choiruddin, “Pemodelan Risiko Gempa Bumi di Pulau Sumatera Menggunakan Model Inhomogeneous Neyman-Scott Cox Process,” J. Sains dan Seni ITS, vol. 9, no. 2, 2021, doi: 10.12962/j23373520.v9i2.52318.
[2] Sunarjo, M. T. Gunawan, and S. Pribadi, Gempabumi Edisi Populer, II. Jakarta: Badan Meteorologi Klimatologi dan Geofisika, 2012.
[3] Kementrian ESDM, Pengenalan Gempa Bumi. Jakarta: Kementrian ESDM, 2013.
[4] Badan Meteorologi Klimatologi dan Geofisika (BMKG), “Rencana Strategis BMKG 2020-2024,” pp. 10–11; 60–63, 2020, [Online]. Available: https://www.bmkg.go.id/profil/?p=rencana-strategis
[5] W. Asnita, D. Sugiyanto, and I. Rusydy, “Kajian Statistik Seismisitas Kawasan Sumatera,” J. Nat., vol. 16, no. 2, 2016.
[6] G. E. P. Box and G. M. Jenkins, Time Series Analysis Forecasting and Control, Revised. Oakland, California: Holden Day, 1976. doi: 10.2307/2284112.
[7] H. H. M. Hatta, F. M. Daud, and N. Mohamad, “An Application of Time Series ARIMA Forecasting Model for Predicting the Ringgit Malaysia-Dollar Exchange Rate,” J. Data Anal., vol. 1, no. 1, pp. 42–48, 2018, doi: 10.24815/jda.v1i1.11884.
[8] H. Nie, G. Liu, X. Liu, and Y. Wang, “Hybrid of ARIMA and SVMs for short-term load forecasting,” in Energy Procedia, 2012, pp. 1455–1460. doi: 10.1016/j.egypro.2012.01.229.
[9] C. Chen, R. A. Davis, and P. J. Brockwell, “Order determination for multivariate autoregressive processes using resampling methods,” J. Multivar. Anal., vol. 57, no. 2, pp. 175–190, 1996, doi: 10.1006/jmva.1996.0028.
[10] J. E. Hanke and D. Wichern, Business Forecasting (Ninth Edition), vol. 5, no. 1. 2014. [Online]. Available: https://ejournal.poltektegal.ac.id/index.php/siklus/article/view/298%0Ahttp://repositorio.unan.edu.ni/2986/1/5624.pdf%0Ahttp://dx.doi.org/10.1016/j.jana.2015.10.005%0Ahttp://www.biomedcentral.com/1471-2458/12/58%0Ahttp://ovidsp.ovid.com/ovidweb.cgi?T=JS&P
[11] D. N. Gujarati and D. J. Porter, Dasar-Dasar Ekonometrika, 5th ed. Jakarta: Salemba Empat, 2013.
[12] A. F. Salaam, W. Somayasa, and M. K. Djafar, “Estimasi Parameter Genetik Gamma Untuk Sampel Tersensor Tipe I dan Tipe II,” J. Mat. Komputasi dan Stat., vol. 3, no. 1, pp. 238–244, 2023, [Online]. Available: http://jmks.uho.ac.id/index.php/JMKS
[13] I. Ghozali, Aplikasi Analisis Multivariete Dengan Program IBM SPSS 23, 8th ed. Semarang: Badan Penerbit Universitas Diponegoro, 2016.
[14] G. E. P. Box and D. A. Pierce, “Distribution of residual autocorrelations in autoregressive-integrated moving average time series models,” J. Am. Stat. Assoc., vol. 65, no. 332, pp. 1509–1526, 1970, doi: 10.1080/01621459.1970.10481180.
[15] A. Hidayat, “Uji Normalitas dan Metode Perhitungan (Penjelasan Lengkap),” Statiskian.com. Accessed: Jun. 04, 2024. [Online]. Available: https://www.statistikian.com/2013/01/uji-normalitas.html
[16] J. Barkus and C. Yavorsky, Understanding and using advanced statistics. London: Sage Publications, Inc, 2006.
[17] R. J. Hyndman and G. Athanasopoulos, Forecasting: Principles and Practice, 2nd ed. 2018. [Online]. Available: https://otexts.com/fpp2/arima-forecasting.html
[2] Sunarjo, M. T. Gunawan, and S. Pribadi, Gempabumi Edisi Populer, II. Jakarta: Badan Meteorologi Klimatologi dan Geofisika, 2012.
[3] Kementrian ESDM, Pengenalan Gempa Bumi. Jakarta: Kementrian ESDM, 2013.
[4] Badan Meteorologi Klimatologi dan Geofisika (BMKG), “Rencana Strategis BMKG 2020-2024,” pp. 10–11; 60–63, 2020, [Online]. Available: https://www.bmkg.go.id/profil/?p=rencana-strategis
[5] W. Asnita, D. Sugiyanto, and I. Rusydy, “Kajian Statistik Seismisitas Kawasan Sumatera,” J. Nat., vol. 16, no. 2, 2016.
[6] G. E. P. Box and G. M. Jenkins, Time Series Analysis Forecasting and Control, Revised. Oakland, California: Holden Day, 1976. doi: 10.2307/2284112.
[7] H. H. M. Hatta, F. M. Daud, and N. Mohamad, “An Application of Time Series ARIMA Forecasting Model for Predicting the Ringgit Malaysia-Dollar Exchange Rate,” J. Data Anal., vol. 1, no. 1, pp. 42–48, 2018, doi: 10.24815/jda.v1i1.11884.
[8] H. Nie, G. Liu, X. Liu, and Y. Wang, “Hybrid of ARIMA and SVMs for short-term load forecasting,” in Energy Procedia, 2012, pp. 1455–1460. doi: 10.1016/j.egypro.2012.01.229.
[9] C. Chen, R. A. Davis, and P. J. Brockwell, “Order determination for multivariate autoregressive processes using resampling methods,” J. Multivar. Anal., vol. 57, no. 2, pp. 175–190, 1996, doi: 10.1006/jmva.1996.0028.
[10] J. E. Hanke and D. Wichern, Business Forecasting (Ninth Edition), vol. 5, no. 1. 2014. [Online]. Available: https://ejournal.poltektegal.ac.id/index.php/siklus/article/view/298%0Ahttp://repositorio.unan.edu.ni/2986/1/5624.pdf%0Ahttp://dx.doi.org/10.1016/j.jana.2015.10.005%0Ahttp://www.biomedcentral.com/1471-2458/12/58%0Ahttp://ovidsp.ovid.com/ovidweb.cgi?T=JS&P
[11] D. N. Gujarati and D. J. Porter, Dasar-Dasar Ekonometrika, 5th ed. Jakarta: Salemba Empat, 2013.
[12] A. F. Salaam, W. Somayasa, and M. K. Djafar, “Estimasi Parameter Genetik Gamma Untuk Sampel Tersensor Tipe I dan Tipe II,” J. Mat. Komputasi dan Stat., vol. 3, no. 1, pp. 238–244, 2023, [Online]. Available: http://jmks.uho.ac.id/index.php/JMKS
[13] I. Ghozali, Aplikasi Analisis Multivariete Dengan Program IBM SPSS 23, 8th ed. Semarang: Badan Penerbit Universitas Diponegoro, 2016.
[14] G. E. P. Box and D. A. Pierce, “Distribution of residual autocorrelations in autoregressive-integrated moving average time series models,” J. Am. Stat. Assoc., vol. 65, no. 332, pp. 1509–1526, 1970, doi: 10.1080/01621459.1970.10481180.
[15] A. Hidayat, “Uji Normalitas dan Metode Perhitungan (Penjelasan Lengkap),” Statiskian.com. Accessed: Jun. 04, 2024. [Online]. Available: https://www.statistikian.com/2013/01/uji-normalitas.html
[16] J. Barkus and C. Yavorsky, Understanding and using advanced statistics. London: Sage Publications, Inc, 2006.
[17] R. J. Hyndman and G. Athanasopoulos, Forecasting: Principles and Practice, 2nd ed. 2018. [Online]. Available: https://otexts.com/fpp2/arima-forecasting.html