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GARCH models capture positive serial correlation in volatility. Sometimes events occur "out of the blue", causing volatility that a GARCH model cannot be expected to predict. One example is the S&P 500 falling 4.37% on December 8, 1941, the day after Pearl Harbor. Another is the U.S. market falling about 10% at the reopening 1 week after the 9/11 attacks.

How should the GARCH estimation procedure be modified, if at all, in the presence of exogenous events? Just remove the "shock" days from the likelihood function? Doing so is plausible but could bias the unconditional variance downward, since such shocks will occur in the future.

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  • $\begingroup$ In general, you should include all information (ie. also the exogenous events) within the estimation procedure. Will your GARCH model fully capture the future spike in volatility implied by the negative returns from the exogenous events (leverage effect)? Probably not. The negative price shocks (very often implied by exogenous market events) contributes to the future spike in volatility, which can be modeled following the GJR-GARCH model. The GJR-GARCH model offers everything the GARCH has to offer, plus a parameter to capture the leverage effect. I don't know, if this answers your question. $\endgroup$
    – Pleb
    Dec 27 '20 at 23:20

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