We investigated the impact of alternative variance equation specifications and different densities on the forecasting of one-day-ahead value-at-risk for the Istanbul stock market. The three employed models are symmetric GARCH(1,1) of Bollerslev (1986), symmetric GARCH(1,1) of Taylor (1986) and APGARCH(1,1) of Ding et al. (1996) models, under three distributions. The comparison focuses on two different aspects: the difference between symmetric and asymmetric GARCH (i.e., GARCH versus APGARCH) and the difference between normal-tailed and fat-tailed distributions (i.e., Normal, Student-t, and GED). The GARCH(1,1) of Taylor was found to be unjustified since convergence could not be achieved. Also, we examined if the estimated coefficients are time-varying. We executed a fixed size rolling sample estimation to provide the one-step-ahead variance forecasts required to generate the one-step-ahead VaR. Our results indicate that the APGARCH(1,1) with t-distribution model outperform its competitors regarding out-of-sample forecasting ability. Moreover, we found that the power transformation parameter of APGARCH model was time-variant. In contrast, degrees of freedom of t-distribution and thickness parameter of GED distribution are time-invariant indicating that fat-tailedness of innovation does not change over time. Thus, these findings suggest that the student-t APGARCH(1,1) model could be used by conservative investors to evaluate their investment risk. Also, both exchanges and regulators may benefit from using that model when the market faces turmoil and becomes more volatile. |
