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Journal : Journal of Mathematics, Computation and Statistics (JMATHCOS)

Forecasting PT Pertamina Geothermal Energy TBK (PGEO) Share Prices using the Arch-Garch Model Ramadhan, Ramadhan; Yurinanda, Sherli; Sarmada, Sarmada
Journal of Mathematics, Computations and Statistics Vol. 8 No. 2 (2025): Volume 08 Nomor 02 (Oktober 2025)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcos.v8i2.9493

Abstract

This study focuses on forecasting the daily closing price of PT Pertamina Geothermal Energy Tbk (PGEO) stocks, recognizing the non-stationary and volatile nature of financial time series data. Traditional forecasting methods, such as the ARIMA (Autoregressive Integrated Moving Average) model, are often insufficient for such data because they rely on the assumption of homoscedasticity, or constant variance in the residuals. An analysis of PGEO's daily stock prices from November 2023 to July 2024 revealed significant fluctuations, indicating the presence of heteroscedasticity, where the variance of the residuals is not constant. In tackling this problem, the study utilized the ARCH (Autoregressive Conditional Heteroskedasticity) and GARCH (Generalized Autoregressive Conditional Heteroskedasticity) frameworks, purpose-built to identify and model the phenomenon of volatility clustering within financial datasets. By integrating the ARIMA model with GARCH, the study aimed to create a more robust forecasting tool. After testing various combinations, the MA(1)–GARCH(1,1) model was identified as the most suitable for predicting PGEO's stock prices. This model successfully captured the fluctuating volatility and produced a highly accurate forecast, as evidenced by a Mean Absolute Percentage Error (MAPE) of just 2.97%. A MAPE value below 10% is generally considered to represent a very high level of forecasting accuracy, confirming the effectiveness of the chosen model in providing reliable short-term predictions for stock market movements. Keywords: ARCH-GARCH, Stock price forecasting, ARIMA
Co-Authors Afrizal Tanjung Ahmad, Amirzah Aisyah Nurbaiti Aji, Kartika Restu Akhmad Qashlim, Akhmad Alfian Hamsi ALI WARDHANA Almira Keumala Ulfah Amun Amri Andi Hasriadi Hasyim Aprilia, Rochmathul Duwi AR, Silvia Arief Agus Triansyah Asrul Nirman Astuti - Aulia, Syahirah Chanda Az-zahra, Caesaria Azizah, Ghina Bahtiar Bahtiar Binti Hamit, Anis Aqilla Brahma, Bayu Budi, Mutiara Setia Budiyono, Slamet Bungkes, Panetir Bunkes, Panetir Cahyati, Martyana Dwi Casiman Sukardi Comeron, Rion Cristo, Natanael Damayanti, Nurul Darwin Lie Dawi Karomati Baroroh Dawolo, Kristiani Delfianti, Delfianti DENNI JOKO PURWANTO, DENNI JOKO Destri Muliastri Dien, Alban W Efendi Efendi Eimar, Cut Rachel Elizal, Elizal Entin Daningsih Ernawati, Wa Fadillawaty Saleh, Fadillawaty Feri Candra Firmansyah, Muhammad Wahyu Fitria Amalia Gautama, Walta Ginawang, Asto Hakas Prayuda Hardiansyah, Fahrudin Hasanudin, La Hayati, Husna Heny Rofizar Hermanto, Cahyo Hersanto Fajri Husein, Abdul Muhaimin Iskandar, Bob Andinata Ismail Ismail Ismail, Sherif Mohamed Iyan Nurdiyan Haris Izhar Salim Johanes Fernandes Andry Jumariyah, Siti Junaidi, Rifqi Junaidi Junianto, Pilifus Kadir Kadir Kadriyani, Emilda kesumah, priatna Kurnia Ningsih Kurniawan, Febriyanto Mahwiyah, Mahwiyah Marfi Yosnita Maruf, Irma Rachmawati Marzuki Marzuki Mohammad Hamdani, Mohammad Mohammad Lutfi Monika, Fanny Muhammad Fajar Purnama Muhammad Halim Pohan Muhammad Handi Pratama Muhammad Hasan Muhammad Iqbal Muhammad Zaini Ngatmin Ningrum, Cahaya Nugroho, Febriawan Ardi Nurdin Nurdin Oktapani, Silm Putri Tipa Anasi Rachmad Imbang Trittjahjono Rahma Nurzianti, Rahma Ranti, Bryen Yuzac Zein Baneka Ratna Sari Dewi Ria Kasmeri Robert Tua Siregar Rustiyarso, Rustiyarso Sabatini, Nafilla Nesantya Salbiyah, Salbiyah Sarmada, Sarmada Sasmita Sasmita Satrya Fajar Kusuma, Fitrah Savitri, Asmah Siti Nurjanah Siti Rohani Sofiyan Sofyan, Rian Fabian Sugiarto S Suhendar, Bagus Sulistyarini, Sulistyarini Sulistyo, Anggi Supartini, Sri Syafrizal Syafrizal Syuhadi Syuhadi Tamin, Rosmawati Tay, En Tedi Rusman Umayasari, Silvia Valentine, Chelsea Rizky Vishnu Juwono, Vishnu Yelmida Azis Yeni, Rahma Yokhebed Yokhebed Yosephine, Satya Howen Yulianti, Eka Budi Yun Gemilang Yurinanda, Sherli Yusanti, Indah Anggraini Yusria Darma Zulfah Zulfah