# Measure how different forecasted volatility is from realized volatility

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 larger 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 package.

Sincerely Yours, Donny