Claim Missing Document
Check
Articles

Found 2 Documents
Search

EARTHQUAKE FREQUENCY DATA MODELING IN MENTAWAI USING FUZZY TIME SERIES LEE AND FUZZY TIME SERIES TSAUR Damayanti, Septri; Rizal, Jose; Yosmar, Siska; Afandi, Nur; Acnesya, Vivin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss1pp0281-0294

Abstract

The Fuzzy Time Series (FTS) was first studied by Song and Chissom based on the theory of fuzzy sets and the concept of linguistic variables and their applications discovered by Zadeh. FTS has several models, namely FTS Lee, FTS Tsaur, and so on. In this study, we will model earthquake frequency data in Mentawai using FTS Lee and FTS Tsaur. The seismicity data used in this study is earthquake frequency data in the Mentawai which are calculated from 1960 to 2022. Additionally, the seismicity data source is taken from the U.S. Geological Survey catalog. Based on MAPE and MSE, the results obtained on the FTS Lee and FTS Tsaur models are MAPE values of 37,511% and 27,051%. And the MSE values obtained were 27,073 and 11,671. Thus, the best model used in modeling data on the frequency of earthquake occurrences in the Mentawai Islands is the Ruey Chyn Tsaur Fuzzy Time Series model.
Pemodelan Return Harga Emas Dengan Pendekatan Inferensi Bayesian ARFIMA Acnesya, Vivin; Devianto, Dodi; Maiyastri
Lattice Journal : Journal of Mathematics Education and Applied Vol. 5 No. 1 (2025): Juni 2025
Publisher : Universitas Islam Negeri Sjech M. Djamil Djambek Bukittinggi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30983/lattice.v5i1.9403

Abstract

Volatility in stock and commodity prices, such as gold, plays a crucial role in investment decisions because high price fluctuations increase risk but also create opportunities for higher returns. The Autoregressive Fractionally Integrated Moving Average (ARFIMA) model, an extension of the ARIMA model, is capable of modeling data with long-term dependencies (long memory). This study applies the Bayesian ARFIMA inference model to address parameter uncertainty by incorporating prior information. The study focuses on modeling monthly gold price returns from January 2014 to December 2024, totaling 132 observations. According to Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values, the Bayesian ARFIMA model achieves slightly better performance with an AIC of -475.2392 and BIC of -469.6136, compared to the ARFIMA model’s AIC of -474.7184 and BIC of -468.968. Gold returns exhibit a long memory characteristic, meaning current price fluctuations can have persistent effects over time. Therefore, investing in gold is highly profitable as it preserves asset value and provides stability against economic volatility.   Volatilitas harga saham dan komoditas, seperti emas merupakan salah satu faktor penting dalam proses pengambilan keputusan investasi, karena fluktuasi harga yang tinggi dapat meningkatkan risiko sekaligus menciptakan peluang untuk memperoleh keuntungan yang lebih besar. Dalam analisis deret waktu (time series), model Autoregressive Fractionally Integrated Moving Average (ARFIMA) merupakan pengembangan dari model Autoregressive Integrated Moving Average (ARIMA) yang mampu memodelkan data dengan ketergantungan jangka panjang (long memory). Penelitian ini menggunakan model inferensi Bayesian ARFIMA untuk mengatasi ketidakpastian pada parameter dengan memanfaatkan informasi prior yang diperoleh. Fokus penelitian adalah pemodelan return harga emas bulanan periode Januari 2014 hingga Desember 2024 dengan total 132 data. Berdasarkan perhitungan Akaike Information Criterion (AIC) dan Bayesian Information Criterion (BIC), model Bayesian ARFIMA memperoleh nilai AIC sebesar -475.2392 dan BIC sebesar -469.6136, sedikit lebih baik dibandingkan model ARFIMA yang memiliki AIC -474.7184 dan BIC -468.968. Harga return emas mengandung sifat long memory yang artinya bahwa fluktuasi harga yang terjadi saat ini dapat memiliki pengaruh yang bertahan dalam jangka panjang, sehingga investasi dalam bentuk emas menjadi sangat menguntungkan karena mampu menjaga nilai aset dari waktu ke waktu dan memberikan stabilitas terhadap gejolak ekonomi.