Pertamina Geothermal Energy Stock Price Prediction and Risk Analysis: ARIMA-GARCH and VaR with Cornish-Fisher Expansion

M. Fariz Fadillah Mardianto; Doni Muhammad Fauzi; Idrus Syahzaqi; Elly Pusporani

doi:10.31764/jtam.v10i3.37866

Pertamina Geothermal Energy Stock Price Prediction and Risk Analysis: ARIMA-GARCH and VaR with Cornish-Fisher Expansion

M. Fariz Fadillah Mardianto, Doni Muhammad Fauzi, Idrus Syahzaqi, Elly Pusporani

Abstract

The geothermal energy sector makes a strategic contribution to supporting long-term domestic energy sustainability and attracts investor attention due to high market volatility. Therefore, analysis that can accurately describe stock price dynamics and risks is needed. This study aims to model and predict the share price of PT Pertamina Geothermal Energy (PGEO) and estimate the associated investment risk. This study uses a quantitative time series approach with ARIMA–GARCH modeling and the Value at Risk method using Cornish–Fisher Expansion. This study uses weekly closing price data for PGEO stocks from February 2023 to September 2025. The methods used include ARIMA-GARCH modeling for stock price prediction and Cornish–Fisher Expansion based Value at Risk to estimate investment risk. The results indicate that the ARIMA(2,2,0)–GARCH(2,0) model provides the most adequate representation of PGEO stock price dynamics and volatility, achieving an RMSE value of 258.33 and a MAPE of 16.21% as measures of forecasting performance. Meanwhile, risk measurement using the Cornish–Fisher Expansion Value at Risk method produced a VaR value that increased along with the holding period and confidence level, with a risk range of 8.21% to 19.95%. The novelty of this research lies in the integration of ARIMA–GARCH volatility modeling and the Value at Risk method using Cornish–Fisher Expansion, thereby providing a more comprehensive analytical framework for price prediction and investment risk estimation in renewable energy stocks. The findings of this study are expected to serve as an empirical reference for investors and policymakers in assessing potential risks and supporting more informed investment decisions within the renewable energy sector.

Keywords

ARIMA-GARCH; Cornish–Fisher Expansion; Geothermal Energy; Stock Price Prediction; Value at Risk.

Full Text:

DOWNLOAD [PDF]

References

Bakarbessy, L., & Manjaruni, V. A. (2024). Mathematical Model In Determining Optimal Portfolio Using Markowitz Method . Motekar: Journal of Education and Science, 1(2), 117–125.

Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3), 307–327. https://doi.org/10.1016/0304-4076(86)90063-1

Cahyasari, A. D., Sediono, S., Ana, E., Mardianto, M. F. F., Pusporani, E., & Ulyah, S. M. (2023). Pemodelan Nilai Saham Perusahaan Pertambangan di Indonesia Berdasarkan Metode Generalized Autoregressive Conditional Heteroscedasticity (GARCH). MUST: Journal of Mathematics Education, Science and Technology, 8(1), 1–12. https://doi.org/10.30651/must.v8i1.17117

Chai, S., & Zhou, P. (2018). The Minimum-CVaR strategy with semi-parametric estimation in carbon market hedging problems. Energy Economics, 76, 64–75. https://doi.org/https://doi.org/10.1016/j.eneco.2018.09.024

Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987–1007. https://doi.org/10.2307/1912773

Hardi, I., Ringga, E. S., Idroes, G. M., Astina, C., Muda, U. P., Noviandy, T. R., & Idroes, R. (2025). Green human development in Indonesia: Role of renewable and nonrenewable energy. Chinese Journal of Population, Resources and Environment, 23(3), 397–411. https://doi.org/https://doi.org/10.1016/j.cjpre.2025.07.010

IDX. (2025). 50 Biggest Market Capitalization - Maret 2023. Indonesia Stock Exchange.

Investing.com. (2025). PT Pertamina Geothermal Energy (PGEO). Investing.Com.

Kim, J. H. T., & Kim, H. (2025). Estimating Skewness and Kurtosis for Asymmetric Heavy-Tailed Data: A Regression Approach. In Mathematics (Vol. 13, Issue 16, p. 2694). https://doi.org/10.3390/math13162694

Li, Z., Geng, M., Su, C.-W., & Qin, M. (2025). Turbulent tides: When green energy ambitions collide with brown resilience in the storm of uncertainty. International Review of Economics & Finance, 104, 104689. https://doi.org/https://doi.org/10.1016/j.iref.2025.104689

Ma’arif, S., Dyah Ari Susanti, Dian Tiara Rezalti, Irmaya, A. I., Yunita, L., Damayanti, D., & Wahyuningtyas, Y. F. (2022). A Review of Strategies for Managing Uncertainty in Crude Oil Prices by Indonesian Oil and Gas Companies and the Government. Jurnal Offshore: Oil, Production Facilities and Renewable Energy, 6(2), 68–84. https://doi.org/10.30588/jo.v6i2.1449

Maruddani, D. A. I., & Astuti, T. D. (2021). Risiko dan Strategi Investasi Saham Second Liner Dengan Global Minimum Variance Portfolio. Jurnal Riset Akuntansi Mercu Buana, 7(1), 15–24. https://doi.org/10.26486/jramb.v7i1.1559

Maruddani, D. A. I., & Trimono. (2020). Microsoft Excel Untuk Pengukuran Value at Risk Aplikasi pada Risiko Investasi Saham. Undip Press.

Mills, T. C. (2019). Applied Time Series Analysis A Practical Guide to Modeling and Forecasting. Academic Press.

MNC Sekuritas. (2025). Driving the Energy Transition: PGEO Leads Indonesia’s Geothermal.

Pertamina. (2025). PERTAMINA and PLN Synergize, PGE Partners with PLN IP to Develop a 530 MW Geothermal Project.

Ramayanti, R., Devianto, D., & Alhusna, D. (2023). Pemodelan Arima-Garch untuk Volatilias dan Value At Risk pada Saham PT. Gudang Garam Tbk. Jurnal Lebesgue: Jurnal Ilmiah Pendidikan Matematika, Matematika Dan Statistika, 4(2), 1029–1040. https://doi.org/10.46306/lb.v4i2.373

Rosyidah, H., Maruddani, D. A. I., & Safitri, D. (2024). Analisis Backtesting Untuk Value At Risk Metode Ekspansi Cornish-Fisher dengan Uji Kupiec. Jurnal Gaussian, 13(2), 405–414. https://doi.org/10.14710/j.gauss.13.2.405-414

Rubio, L., Palacio Pinedo, A., Mejía Castaño, A., & Ramos, F. (2023). Forecasting volatility by using wavelet transform, ARIMA and GARCH models. Eurasian Economic Review, 13(3), 803–830. https://doi.org/10.1007/s40822-023-00243-x

Safitri, D., Gunardi, G., Susyanto, N., & Sulandari, W. (2025). SSA-ARIMA-GARCH hybrid model for time series with heteroscedasticity. Mathematical Modelling of Engineering Problems, 12(8), 2661–2668. https://doi.org/https://doi.org/10.18280/mmep.120807

Sekretariat Kabinet RI. (2025). President Prabowo Launches Danantara for Sustainable Investment Management.

Singh, S., Parmar, K. S., & Kaur, J. (2023). Chapter 12 - Forecasting volatility in the stock market data using GARCH, EGARCH, and GJR models (S. Eslamian & F. B. T.-H. of H. Eslamian (eds.); pp. 207–220). Elsevier. https://doi.org/https://doi.org/10.1016/B978-0-12-821285-1.00024-5

Souffargi, W., & Boubaker, A. (2025). Modelling Value-at-Risk and Expected Shortfall for a Small Capital Market: Do Fractionally Integrated Models and Regime Shifts Matter? In Journal of Risk and Financial Management (Vol. 18, Issue 4, p. 203). https://doi.org/10.3390/jrfm18040203

Wang, X., Vigne, S. A., & Huang, S. (2025). The impact of uncertainties on contagions in energy market risk networks: Evidence from synthesizing multiple-order moments and multiple time horizons. International Review of Economics & Finance, 102, 104312. https://doi.org/https://doi.org/10.1016/j.iref.2025.104312

Wang, Y., Xiang, Y., Lei, X., & Zhou, Y. (2022). Volatility analysis based on GARCH-type models: Evidence from the Chinese stock market. Economic Research-Ekonomska Istraživanja, 35(1), 2530–2554. https://doi.org/10.1080/1331677X.2021.1967771

Wei, W. S. (2006). Time Series Analysis Univariate and Multivariate Methods (2nd ed.). Pearson Education.

DOI: https://doi.org/10.31764/jtam.v10i3.37866