LeveragingEgarchEgarch – the model (compare parameterization that of Splus)Other variants – Splus documentation (Zivot)K. Ensor, STAT 4211Spring 2004Leveraging•Bad news – negative shocks – have a larger impact on volatility than good news or positive shocks.•This asymmetry is incorporated in a GARCH framework by the inclusion of a “leverage” effect.K. Ensor, STAT 4212Spring 2004EgarchThe exponential GARCH formulation models the log of the conditional variance as an ARMA structure with asymmetric innovations.An advantage of modeling the “log” of the process – variances are guaranteed to be positive.K. Ensor, STAT 4213Spring 2004Egarch – the model (compare parameterization that of Splus)0)(|))((|)()(0)(|))((|)()(|)])((||)([|)())1(())1((11)ln()()()()()(102ttEtttEttEtttgtgBBBBttatattrmmssttK. Ensor, STAT 4214Spring 2004Other variants – Splus documentation (Zivot)•Power GARCH – return to modeling the conditional variance.•Consider other behaviors the “squared GARCH behavior”.•Threshold GARCH – set a threshold for different models to kick in (leveraging is
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