GARCH models with leverage effect : differences and similarities

Abstract

In this paper, we compare the statistical properties of some of the most popular GARCH models with leverage e?ect when their parameters satisfy the positivity, stationarity and nite fourth order moment restrictions. We show that the EGARCH speci cation is the most exible while the GJR model may have important limitations when restricted to have nite kurtosis. On the other hand, we show empirically that the conditional standard deviations estimated by the TGARCH and EGARCH models are almost identical and very similar to those estimated by the APARCH model. However, the estimates of the QGARCH and GJR models di?er among them and with respect to the other three speci cations.