ARFIMA Modelling for Tectonic Earthquakes in The Maluku Region
Pemodelan ARFIMA untuk Kejadian Gempa Bumi Tektonik di Wilayah Maluku
Keywords:Maluku Province, Earthquakes, Tectonic, ARFIMA Model, MSE
Maluku Province is one of the regions in Indonesia with a very active and very prone earthquake intensity because it is a meeting place for 3 (three) plates, namely the Eurasian, Pacific and Australian plates. In the last 100 years, the history of tectonic earthquakes with tsunamis that occurred in Indonesia was 25-30% occurring in the Maluku Sea and Banda Sea. Based on this fact, this study aims to analyze the incidence of tectonic earthquakes that occurred in the Maluku region and its surroundings using the Autoregressive Fractionally Integrated Moving Averages (ARFIMA) model which has the ability to explain long-term time series data (long memory). The results of the research data analysis show that the best model for predicting the number of tectonic earthquakes that occur in Maluku and its surroundings is ARFIMA (0; 0.712; 1) with an MSE value of 0.1156. Meanwhile, the best model for predicting the average magnitude of the number of tectonic earthquakes that occurred in Maluku and its surroundings is ARFIMA (0; -3,224 x 10-9; 1) with an MSE value of 0.01237. Based on the two best models, the prediction results obtained from the number of tectonic earthquakes and the average magnitude of the number of tectonic earthquakes that occurred in Maluku and its surroundings for the next three periods, namely the first period there were 31 tectonic earthquakes with an average magnitude of 4.38481 SR. the second period there were 32 tectonic earthquakes with an average magnitude of 4.38407, and the third period there were 32 tectonic earthquakes with an average magnitude of 4.38333.
Hartini, D. & Nurmaleni. (2018). Penerapan Model Autoregressive Fractionally Integrated Moving Average (ARFIMA) dalam Prakiraan Data Suku Bunga PUAB (Pasar Uang Antar Bank). Jurnal Logika 8(1) : 24-35
Ishida, I & Watanabe, T. (2008). Modelling And Forecasting The Volatility Of The Nikkei 225 Realized Volatility Using The ARFIMA GARCH Model. Global COE Hi-Stat Discussion Paper Series 032 :1-24.
Nugraha, J., Mawaleda, M., Farida, M., Rohadi, M. S., Sadly, M., and Karnawati, D. (2019). Pulau Seram dan sekitarnya Menyimpan Potensi Gempabumi Tektonik dalam Skala Besar. Badan Meteorologi Klimatologi dan Geofisika.
Palma, W. (2007). Long-Memory Time Series Theory and Methods. John Wiley & Sons, Inc : New Jersey.
Rizal, J., Nugroho, S., Irwanto, A., and Debora. (2016). Analisis Kejadian Gempa Bumi Tektonik Di Wilayah Pulau Sumatera. Jurnal Matematika 6 (1) :1-14.
Sari, A. P. (2017). Perbandingan Aplikasi Model ARIMA dan ARFIMA Pada Kasus Data Harga Saham PT. Telekomunikasi Indonesia Persero. Skripsi. Program Sarjana Jurusana Matematika. Fakultas MIPA. Universitas Negeri Malang.
Siew, L.Y., Chin, L. Y., and Pauline, M. J.W. (2008). ARIMA and Integrated ARFIMA Models For Forecasting Air Pollution Index In Shah Alam, Selangor. The Malaysian Journal Of Mathematics Science 2 (2) : 41-54
Sinay, L. J., Lembang, F.K., Aulele, S. N., and Mustamu, D. (2020). Analisis Curah Hujan Bulanan Di Kota Ambon Menggunakan Model Heterokedastisitas : SARIMA-GARCH. Jurnal Media Statistika 13 (1) : 68-79.
Wattimanela, H.J. & Latupeirissa, S. J. (2020). Analysis of Tectonic Earthquake Characteristics in The Province Of Nusa Tenggara Barat Indonesia and its Surroundings. IOP Conf. Series : Journal of Physics : Conf Series 1463(2020) 012002. doi:10.1088/1742-6596/1463/1/012002.
Wei, W. W. (2006). Time Series Analysis Univariate and Multivariate Methods. Second Edition. Greg Tobin : USA.