Penerapan Model Autoregressive Fractionally Integrated Moving Average (ARFIMA) dalam Memprediksi Banyak Gempa Bumi di Barat Pulau Jawa
Abstract
Abstract. Autoregressive Fractionally Integrated Moving Average (ARFIMA) is capable of describing both short and long-memory time series through the use of fractional differencing (d) values. This study aims to apply the ARFIMA (p,d,q) model to predict the frequency of earthquakes in west of Java, Indonesia, in upcoming periods. Utilizing secondary data from United States Geological Survey (USGS) spanning from 1971 to 2023, the parameters (p,q) were estimated using the maximum likelihood estimation method, while the differencing parameter (d) was estimated using the Rescaled Range Statistics (R/S) method, resulting in d = 0,273. The best fit model was ARFIMA (1;d;1) with the equation (1-〖〖∅_1 B)(1-B)〗^0,273 Z〗_t=θ_1 (B) e_t and with an AIC value of 110,883. The model predicts 7 future periods, indicating a general increase in earthquake activity in west of Java, although fluctuations in the predictions suggest a tendency towards decreasing volatility.
Abstrak. Autoregressive Fractionally Integrated Moving Average (ARFIMA) mampu menjelaskan runtun waktu jangka pendek (short memory) maupun jangka panjang (long memory) dengan nilai differencing (d) bernilai pecahan. Tujuan utama penelitian ini adalah bagaimana penerapan model ARFIMA (p,d,q) dalam memprediksi banyak gempa bumi di barat Pulau Jawa pada periode selanjutnya. Menggunakan data sekunder USGS (United States Geological Survey) tahun 1971-2023, estimasi parameter (p,q) menggunakan metode maximum likelihood d dan estimasi parameter differencing (d) dengan metode analisis Rescaled Range Statistics (R/S) memberikan hasil d=0,273, dimana model terbaik terpilih adalah ARFIMA(1;d;1) dengan persamaan model (1-〖〖∅_1 B)(1-B)〗^0,273 Z〗_t=θ_1 (B) e_t dan nilai AIC sebesar 110,883 yang menghasilkan 7 periode prediksi dengan pergerakan kejadian gempa bumi di barat Pulau Jawa relatif meningkat meskipun fluktuasi prediksi cenderung menurun.
References
Maryanto Rompon, Hamim Tsalis Soblia, Putri Monika, Atje Setiawan Abdullah, Budi Nurani Ruchjana. Identifikasi Autokorelasi Spasial Warisan Budaya Tak Benda di Indonesia Menggunakan Indeks Moran. Statistika. 2023 Dec 11;23(2):156–63.
Badan Geologi Pusat Vulkanologi dan Mitigasi Bencana Geologi. Badan Geologi Pusat Vulkanologi dan Mitigasi Bencana Geologi. 2022. Laporan dan Rekomendasi Teknis Gempa Bumi Tanggal 21 November 2022 di Kabupaten Cianjur, Provinsi Jawa Barat.
BNPB. Badan Nasional Penanggulangan Bencana. 2022 [cited 2023 May 23]. Kerusakan Bangunan AKibat Gempabumi M5,6 Cianjur. Available from: https://www.bnpb.go.id/berita/kerusakan-bangunan-akibat-gempabumi-m5-6-cianjur
Shalsadilla N, Martha S, Perdana H, Satyahadewi N, Sulistianingsih E, Program ), et al. Penentuan Jumlah Cluster Optimum Menggunakan Davies Bouldin Index dalam Pengelompokan Wilayah Kemiskinan di Indonesia [Internet]. Vol. 23. 2023. Available from: https://bps.go.id
Hananti H, Jaya IGNM, Irlandia Ginanjar. Pemodelan Kasus Gizi Buruk Balita di Indonesia Menggunakan Panel Quantile Regression Model. Statistika. 2023 Nov 23;23(2):116–22.
Jose Rizal, Sigit Nugroho, Adi Irwanto. Analisis Kejadian Gempa Bumi Tektonik di Wilayah Pulau Sumatera. Jurnal Matematika. 2016;1–14.
H J Wattimanela, S J Latupeirissa. Analysis of Tectonic Earthquake Characteristics in The Province of Nusa Tenggara Barat Indonesia and Its Surroundings. J Phys Conf Ser. 2020;
USGS. United State Geological Survey . USGS (United State Geological Survey) .
Box GEP, Jenkins GM, Reinsel GC, Ljung GM. Time Series Analysis Forecasting And Control. Vol. 5. 2016.
Wei WWS. Time Series Analysis-Univariate and Multivariate Methods. Vol. 2. 2006.
Draper NR, Smith H. Applied Regression Analysis, Third Edition. Vol. 3. 1998.
Montgomery DC, Jennings CL, Kulahci M. Introduction To Time Series Analysis And Forecasting. second. Canada: John Wiley & Sons, Inc., Hoboken, New Jersey.; 2019.
Kartikasari P. Studi Simulasi Pengaruh Outlier terhadap Pengujian Linieritas dan Long Memory beserta Aplikasinya pada Data Return Saham. Surabaya; 2015.
Kartikasari P, Yasin H, Asih I Maruddani D. ARFIMA Model for Short Term Forecasting of New Death Cases COVID-19. In: E3S Web of Conferences. EDP Sciences; 2020.
Hosking JRM. Fractional differencing. Biometrika. 1981;68(1):165–76.
Mcleod AI, Yu H, Krougly ZL. Algorithms for Linear Time Series Analysis: With R Package. J Stat Softw [Internet]. 2007;23(5). Available from: http://www.jstatsoft.org/
Yanti TS. Analisis Deret Waktu. Vol. 1. Pustaka Ceria, Yayasan PENA; 2010.
J.Q. Veenstra, A.I. McLeod. Package “arfima” Fractional ARIMA (and Other Long Memory) Time Series Modeling [Internet]. cran.r-project.org. cran.r-project.org; 2022 [cited 2023 Sep 14]. Available from: https://cran.r-project.org/web/packages/arfima/index.html
