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How do you fit a GARCH model to the returns of a stock given the dates of past earnings announcements? Volatility will tend to higher than a GARCH model would predict on the announcement day.

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You can fit a GARCH model with exogenous dummy variables included in the equation for the conditional variance. E.g. if there have been $m$ announcements in the past, then $$ \sigma_{t}^2 = \omega + \alpha_1\varepsilon_{t-1}^2 + \beta_1\sigma_{t-1}^2 + \sum_{i=1}^m\gamma_i d_i $$ where $d_i$ is a dummy variable corresponding to the $i$th announcement.

(If you have reason to believe each announcement had the same effect on the conditional variance, then you can substitute $\sum_{i=1}^m\gamma_i d_i$ with $\tilde d_i$ where $\tilde d_i$ is a dummy that equals one on the announcement days and zero otherwise. This way you would reduce estimation variance at a risk of introducing some bias. But if you are modeling earnings announcements, the assumption of equal effects does not seem realistic, as the announcements are not all the same. Then the bias introduced this way might well outweigh any reduction in variance.)

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  • $\begingroup$ On the RHS I think the subscript of sigma should be t-1, not t. I tried to fix it, but edits are supposed to be at least 6 characters. $\endgroup$
    – Fortranner
    Oct 23, 2022 at 11:34
  • $\begingroup$ @Fortranner, thank you for spotting this typo. I guess I made it by copying and pasting from the left hand side of the equation. Now fixed. $\endgroup$ Oct 23, 2022 at 13:00
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A relevant working paper is Forecasting Market Volatility: The Role of Earnings Announcements

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