Value-at-Risk Analysis of PT Bukit Asam Tbk (PTBA) Stock Returns Based on an ARIMA–GARCH Model with a Student-t Distribution

Najwa Khoir Aldawiyah (Departement of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia)
Indana Zulfa Wulandari (Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia)
Ahmad Wahyu Firmanda (Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia)
M. Fariz Fadillah Mardianto (Statistical Modelling for Economic and Social Sciences Research Group, Departement of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia)

JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Vol. 22 No. 3 (2026): May 2026

Stock investment involves substantial risk due to return volatility, which is particularly evident in mining sector stocks such as PT Bukit Asam Tbk (PTBA). This study aims to estimate stock return risk under high volatility and leptokurtic behavior using an ARIMA–GARCH model with a Student-t distribution, focusing on Value-at-Risk (VaR) as a risk measure. Daily PTBA stock return from closing price data from 1 October 2024 to 3 November 2025 were obtained from Investing.com. The best model is ARIMA (0,1,1)–GARCH-t (1,1), with an AIC value of −5.612 and a testing MSE of 0.0000127. The Student-t VaR is estimated at 0.023188 (95%) and 0.046318 (99%), while the Cornish–Fisher approach yields higher VaR values of 0.032674 (95%) and 0.12472 (99%). These results indicate that heavy-tailed volatility models provide more prudent risk estimates and are useful for investment risk management under extreme market conditions.