# Question regarding the interpretation of the GARCH coefficients, is it possible to take the logarithms?

The GARCH model I am estimating is

$y_t = \alpha_0 + \epsilon_t$

$\sigma_t^2 = c_0 + c_1 \epsilon^2_{t-1} + \beta \sigma_{t-1}^2 + \delta_0 I + \delta_1 I(-1) + \delta_2I(-2)$

with the output of the estimation here

https://i.imgur.com/xLrbLtg.png

$y_t=\log(p_{t-1}/p_t)$ stands for the logarithmic returns of Google's stock price, and $I$ is a dummy variable that is 1 on an earnings announcement day and 0 on all other days.

I have three questions:

1. Is it bad that I don't take on any $X$ regressors in the mean equation? Looking at the graph of the logarithmic returns it seems (and I've tested) that it's a stationary process, and I purely want to model the variance.

2. I want to estimate the effect that an announcement day has, in terms of volatility. Am I doing this correctly with these dummmies? How can I interpret these dummies?

3. With 'normal' regressions, you can take logs on both sides like $\log(y_t) = \alpha + \beta\log(X) + \epsilon$ to make the interpretation of the results easier (elasticity), is it possible to do something like this with the variance equation in my GARCH model? Like this:

$$\log(\sigma_t^2) = c_0 + c_1\log(\epsilon^2_{t-1}) + \beta \log(\sigma_{t-1}^2) + \delta_0 I + \delta_1 I(-1) + \delta_2I(-2).$$