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

Jurnal Matematika, Statistika dan Komputasi · Vol. 22 No. 3 (2026) · hlm. 546–559

DOI
10.20956/j.v22i3.49505
ISSN
2614-8811, 1858-1382
Terbit
2026-05-14
Penerbit
Department of Mathematics, Hasanuddin University
Bahasa
en
Lisensi
creativecommons.org/licenses/by/4.0

Abstrak

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.

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  • Universitas Airlangga
  • Universitas Islam Madura
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Rekan penulisOrganisasiArtikel bersama
Elly PusporaniUniversitas Airlangga4
Dita AmeliaUniversitas Airlangga4
Pressylia Aluisina Putri WidyanggaAfiliasi tidak diketahui2
Bima Sakti Putra YusufAfiliasi tidak diketahui2
Suliyanto SuliyantoUniversitas Airlangga2
Eko Fajar CahyonoUniversitas Airlangga2
Zalfaa Nur AmaliaUniversitas Airlangga1
Rosyida Widadina UlyaUniversitas Airlangga1
Disty Ridha HastutiUniversitas Airlangga1
Adma Novita SariAfiliasi tidak diketahui1
M. Suma Firman RomadhoniAfiliasi tidak diketahui1
Faisol FaisolUniversitas Islam Madura1
Putri UkhrowiUniversitas Islam Madura1
Ira YudistiraUniversitas Islam Madura1
Kuzairi KuzairiUniversitas Islam Madura1
Muhammad Fikry Al FariziUniversitas Airlangga1
Made Riyo Ary PermanaUniversitas Airlangga1
Alfian Iqbal ZahUniversitas Airlangga1
Bagas Shata PratamaUniversitas Airlangga1
Grace Lucyana KoesnadiUniversitas Airlangga1
Dzuria Hilma Qurotu AinUniversitas Airlangga1
Ardi KurniawanUniversitas Airlangga1
Adnan Syawal Adilaha SadikinUniversitas Airlangga1
Aqil Azmi ReswaraUniversitas Airlangga1
Rosidun Nindyo PratiwiUniversitas Airlangga1
Nathania FauziahUniversitas Airlangga1
Bimo Okta SyahputraUniversitas Airlangga1
Nur ChamidahUniversitas Airlangga1
Toha SaifudinUniversitas Airlangga1
Rien RecyliaUniversitas Airlangga1
Fatiha Nadia SalsabilaUniversitas Airlangga1
Alfi Nur NitasariUniversitas Airlangga1
Irma Ayu IndrastaUniversitas Airlangga1
Hanny ValidaUniversitas Airlangga1
Farah Fauziah PutriUniversitas Airlangga1
M. Nabil SaputraUniversitas Airlangga1

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Sumber metadata: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, pertama di-harvest 5 Nov 2026, terakhir terlihat 8 Nov 2026.
Metadata asli (oai_dc) 
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	<dc:title xml:lang="en">Value-at-Risk Analysis of PT Bukit Asam Tbk (PTBA) Stock Returns Based on an ARIMA–GARCH Model with a Student-t Distribution</dc:title>
	<dc:creator xml:lang="en">Aldawiyah, Najwa Khoir</dc:creator>
	<dc:creator xml:lang="en">Wulandari, Indana Zulfa</dc:creator>
	<dc:creator xml:lang="en">Firmanda, Ahmad Wahyu</dc:creator>
	<dc:creator xml:lang="en">Mardianto, M. Fariz Fadillah</dc:creator>
	<dc:subject xml:lang="en">ARIMA-GARCH</dc:subject>
	<dc:subject xml:lang="en">PTBA</dc:subject>
	<dc:subject xml:lang="en">Student-t</dc:subject>
	<dc:subject xml:lang="en">Value at Risk</dc:subject>
	<dc:description xml:lang="en">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.
 
 </dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2026-05-14</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
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	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/49505</dc:identifier>
	<dc:identifier>10.20956/j.v22i3.49505</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 22 No. 3 (2026): May 2026; 546-559</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/49505/14409</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2026 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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