VARIANSI: Journal of Statistics and Its application on Teaching and Research

Perbandingan Model Value-at-Risk (VaR) Hybrid GARCH-EVT dan Model Standar dalam Pengukuran Risiko Ekstrem pada Portofolio Saham Sektoral di Indonesia

Annisa Syalsabila — 2025-12-03

This study aims to construct an optimal portfolio and compare the accuracy of various Value-at-Risk (VaR) models in measuring the risk of stock portfolios in the Indonesia Stock Exchange (IDX). The optimal portfolio is formed using the Minimum Variance Portfolio (MVP) method based on 11 sector-representative stocks for the period 2019–2025. The risk performance of this portfolio is then evaluated using six VaR models: Variance–Covariance (VC), Historical Simulation (HS), Monte Carlo (MC), GARCH (1,1), Extreme Value Theory (EVT-GPD), and the hybrid GARCH–EVT model. Model accuracy is assessed through backtesting using the Kupiec Proportion of Failures (POF) test and the Christoffersen Conditional Coverage (CC) test at the 95% and 99% confidence levels. The optimization results indicate that the MVP portfolio is dominated by defensive sectors such as consumer non-cyclicals (ICBP.JK) and large-cap banking (BBCA.JK). Backtesting results show that although all models perform adequately at the 95% level, standard models (VC, MC, GARCH) fail to capture extreme risk at the 99% level. In contrast, the GARCH–EVT model satisfies the backtesting criteria and emerges as the most accurate and superior model for predicting extreme losses.

Penelitian ini bertujuan untuk membangun portofolio optimal dan membandingkan akurasi berbagai model Value-at-Risk (VaR) dalam mengukur risiko portofolio saham di Bursa Efek Indonesia (BEI). Portofolio optimal dibentuk menggunakan metode Minimum Variance Portfolio (MVP) dari 11 saham perwakilan sektor periode 2019-2025. Kinerja risiko portofolio ini kemudian diukur menggunakan enam model VaR: Variance-Covariance (VC), Historical Simulation (HS), Monte Carlo (MC), GARCH (1,1), Extreme Value Theory (EVT-GPD), dan model hybrid GARCH-EVT. Akurasi model diuji menggunakan backtesting Uji Kupiec (POF) dan Uji Christoffersen (CC) pada tingkat kepercayaan 95% dan 99%. Hasil optimisasi menunjukkan portofolio MVP didominasi oleh sektor defensif seperti consumer non-cyclicals (ICBP.JK) dan perbankan big-cap (BBCA.JK). Hasil backtesting menunjukkan bahwa meskipun semua model akurat pada tingkat 95%, model standar (VC, MC, GARCH) gagal mengukur risiko ekstrem pada tingkat 99%. Sebaliknya, model GARCH-EVT terbukti memenuhi uji dan menjadi model yang paling akurat dan superior untuk memprediksi kerugian ekstrem.

APPLICATION OF TIME SERIES REGRESSION (TSR) AND AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) IN RICE PRODUCTION FORECASTING IN INDONESIA

Muhammad Fahmuddin S — 2025-12-03

Rice production plays a crucial role in supporting food security in Indonesia. The annual fluctuations in rice yield necessitate accurate forecasting methods to support agricultural planning. This study aims to forecast rice production in Indonesia using two time series forecasting approaches: Time Series Regression (TSR) and Autoregressive Integrated Moving Average (ARIMA). The data used consist of monthly rice production from January 2020 to December 2024. The analysis results show that both methods are capable of modeling the data well, with high forecasting accuracy based on the Mean Absolute Percentage Error (MAPE). The TSR model yielded a MAPE of 13.838%, while the ARIMA(2,1,0)(0,1,0)12model achieved a lower MAPE of 13.1439%, indicating that the ARIMA model provides more accurate forecasting results. This study is expected to serve as a reference for policy-making and strategic planning in rice production management in the future.

Analisis Model Volatilitas ARCH/GARCH untuk Mengestimasi Value at Risk pada Data Saham PT Indofood CBP Sukses Makmur Tbk (ICBP)

Muhammad Nusrang — 2025-12-31

Dalam data time series keuangan, volatilitas cenderung tinggi dan ditandai dengan fluktuasi besar, yaitu periode volatilitas tinggi diikuti periode rendah, kemudian kembali meningkat, atau dikenal sebagai masalah heteroskedastisitas. Pemodelan ARIMA Box-Jenkins tidak lagi valid sehingga diperlukan metode alternatif seperti ARCH/GARCH. Penelitian ini bertujuan memodelkan volatilitas harga penutupan saham PT ICBP menggunakan ARCH/GARCH serta mengestimasi nilai risiko investasi dengan Value at Risk (VaR). Hasil analisis menunjukkan bahwa model ARIMA (0,1,1)-ARCH (1) merupakan model terbaik dalam menggambarkan volatilitas saham dengan parameter signifikan dan akurasi peramalan yang cukup baik (MAPE = 5,8%). Estimasi VaR dengan simulasi historis menunjukkan potensi kerugian maksimum harian untuk investasi Rp10.000.000,00 sebesar Rp534,48 pada tingkat keyakinan 90%, Rp541,17 pada 95%, dan Rp546,54 pada 99%. Temuan ini memberikan gambaran jelas mengenai risiko harian yang dapat dijadikan bahan pertimbangan dalam pengambilan keputusan investasi pada saham ICBP.