GARCH MODELS WITH LEVERAGE EFFECT: DIFFERENCES AND SIMILARITIES.

In this paper, we compare the statistical properties of some of the most popular GARCH models with leverage effect when their parameters satisfy the positivity, stationarity and finite fourth order moment restrictions. We show that the EGARCH specification is the most flexible while the GJR model may have important limitations when restricted to have finite 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 differ among them and with respect to the other three specifications