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. |
