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All Journal Journal of Mathematics, Computation and Statistics (JMATHCOS) Indonesian Journal of Fundamental and Applied Geography
Ferigo Taufani Tri Hakiki
Institut Teknologi Sepuluh November
Earth & Planetary Sciences Education Environmental Science Mathematics

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Hybrid ARX–GARCH–LSTM Approach for Volatility Estimation of Indonesia’s Oil and Gas Sector Stocks: A Case Study of PGAS Ferigo Taufani Tri Hakiki; Irhamah Irhamah; Heri Kuswanto
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/rrv0zb05

Abstract

This study develops a hybrid ARX–GARCH–LSTM approach to estimate the volatility of PGAS stock during the 2010–2025 period. Stock volatility exhibits characteristics such as heteroskedasticity, volatility clustering, and nonlinear patterns, requiring an approach capable of capturing volatility dynamics more accurately. The proposed approach integrates the ARX model to capture the influence of external factors, the GARCH model to model time-varying volatility, and Long Short-Term Memory (LSTM) to learn nonlinear patterns from the residual/errors of the GARCH model. The modeling process begins by transforming stock prices into log returns, followed by ARX estimation to purify returns from the influence of exogenous variables. The ARX residuals are then modeled using GARCH(1,1), and the residual/errors generated by the GARCH model are subsequently used as input for the LSTM model to construct the hybrid ARX–GARCH–LSTM model. The results show that the hybrid ARX–GARCH–LSTM model outperforms the GARCH and baseline LSTM models with an RMSE value of 0.004250, an MAE value of 0.003077, and an R² value of 0.827293. Compared to the GARCH model, the hybrid approach reduces RMSE by 42.43% and MAE by 48.53%, while increasing the R² value by 72.83%. These findings indicate that the integration of statistical models and deep learning methods can improve the accuracy of stock volatility estimation and potentially support investment decision-making and financial risk management.
Analysis of Pangkep Regency Groundwater Potential Through the Use of the Overlay Method Geographic Information System Nasrul; Muhammad Taufan Nuryadin; Mulianti; Sri Wahyuni Hasrin; Mat Rasul; Ferigo Taufani Tri Hakiki
Indonesian Journal of Fundamental and Applied Geography Vol. 2 No. 1 (2024)
Publisher : PT. Lontara Digitech Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.61220/ijfag.v2i1.20250

Abstract

The increase in population results in an increase in the amount of water supply needed to carry out all activities of the population.  Groundwater is a very important alternative source, especially during the dry season. This research aims to determine the distribution of groundwater potential in Pangkajene Regency and the islands which can be used as a reference and information regarding areas that have groundwater potential. By using the overlay method through the use of geographic information systems. This method is carried out by scoring each parameter used, namely giving a value and weighting according to the classification of each parameter. The analysis process was carried out with the help of the ArcGIS 10.8 mapping application. Based on the results of the analysis carried out in this research, it was found that Pangkep Regency as a whole has a moderate level of groundwater potential, this can be seen from the percentage of 60.26% of the total area of ​​Pangkajene Regency or around 476.4302954 km2 has groundwater potential. which is being. In this case, the government needs to carry out regular monitoring and evaluation of groundwater conditions in areas with medium potential including Tondong Talassa, Minasa Tene, Pangkajene, and Bungoro sub-districts to ensure that the quality and quantity of groundwater do not decline to low or very low. As well as carrying out detailed exploration and inventory of groundwater potential in areas with high levels such as in the Mandalle, Marang, and Labakkang subdistricts.
Co-Authors Heri Kuswanto Irhamah - Mat Rasul Muhammad Taufan Nuryadin Mulianti Nasrul Sri Wahyuni Hasrin