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Hi Quantitative Finance Stack Exchange,

I'm looking for an opinion on a simple question. Suppose I use a Garch(1,1) model to make a volatility forecast.

At time $t$, I have realized volatility $\sigma_t$ and forecasted volatility $\hat{\sigma}_t$. I understand that strategies commonly use $\hat{\sigma}_t$ to decide on risk management, i.e. liquidate if $\hat{\sigma}_t>10\text{bps}$.

However, I wish to have a measure on when $\hat{\sigma}_t$ is significantly more than $\sigma_t$. I tried the F-test on $\frac{\hat{\sigma}_t}{\sigma_t}$. The degrees of freedom of $\sigma_t$ is the number in samples of $\sigma_t$. What is the degrees of freedom of $\hat{\sigma_t}$?

I'm using R's rugarch.

Sincerely Yours, Donny

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