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In this paper, we analyze five of the most popular models proposed to represent conditional heteroscedasticity with leverage effect, namely, GQARCH, TGARCH, GJR, EGARCH, and APARCH. We show that when the parameters satisfy the positivity, stationarity, and finite kurtosis conditions, the...
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GARCH volatilities depend on the unconditional variance, which is a non-linear function of the parameters. Consequently, they can have larger biases than estimated parameters. Using robust methods to estimate both parameters and volatilities is shown to outperform Maximum Likelihood procedures.
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