Comparing GARCH Volatility Forecasts with Realized Volatility

Summary

The document asks how to assess whether a GARCH(1,1) volatility forecast is significantly above realized volatility. It describes a proposed approach: apply an F-test to the ratio of forecasted and realized volatility, then determine the degrees of freedom for the forecast estimate. The motivation is to distinguish forecasts that may warrant risk controls from forecasts that are unusually high relative to observed volatility.

The text does not provide an answer or establish that an F-test is appropriate. It gives no details about how realized volatility is estimated, the forecast horizon, or the statistical distribution of the forecast, all of which could matter for inference. The question therefore identifies a modeling and testing issue rather than presenting a validated method or empirical evidence.

Key ideas

• The question concerns statistical comparison of GARCH volatility forecasts with realized volatility.
• It proposes an F-test on the ratio of forecasted to realized volatility.
• The degrees of freedom for the forecast estimate are left unresolved.
• The document does not establish that the proposed test is valid.

Tags

# Measure how different forecasted volatility is from realized volatility


# 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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.