Estimating Value at Risk of the Indonesian Sharia Stock Index using Asymmetric GARCH-MIDAS

Abstract

This study estimates the market risk of the Indonesian Sharia Stock Index (ISSI) using a volatility framework that combines short-run asymmetric GARCH dynamics and long-run macroeconomic information through the GARCH-MIDAS approach. Daily ISSI closing prices are transformed into logarithmic returns, while monthly inflation and BI Rate are used as low-frequency macroeconomic variables in the MIDAS component. The conditional mean is first represented by an ARIMA process, and the residual variance is then modeled using GARCH(1,1), TGARCH(1,1), GJR-GARCH(1,1), GARCH(1,1)- MIDAS, and GJR-GARCH(1,1)-MIDAS. Value at Risk (VaR) is computed at the 5%, 2.5%, and 1% quantiles, and model adequacy is evaluated with the Kupiec Proportion of Failure (POF) backtesting test. The empirical results show that ISSI returns are stationary around zero, while the closing price series displays a long-run increasing trend with sharp corrections during stress periods. The return series exhibits volatility clustering, ARCH effects, and asymmetric volatility, supporting the use of asymmetric GARCH specifications. The ARIMA(0,0,0) model is selected as the mean model, while GJR-based models provide stronger evidence of leverage effects in the conditional variance. The MIDAS results indicate that inflation and BI Rate are not statistically significant determinants of the long-run volatility component at the 5% level, suggesting that short-run market shocks dominate the volatility process during the sample period. The Kupiec POF results indicate that GJR-GARCH-MIDAS models with inflation and BI Rate are accepted at the 2.5% and 1% VaR quantiles, making them the most consistent specifications for downside risk estimation of ISSI. The findings confirm that incorporating asymmetric volatility is important for improving VaR estimation in the Indonesian Islamic equity market.