Adding VIX Regressors to GARCH Variance Models in R

Summary

The document discusses modeling S&P 500 return volatility with GARCH models that use the VIX as an external regressor. The question concerns comparing GARCH forecasts with implied volatility forecasts, using data from 2020 through 2022, and asks whether to lag the VIX and include a variance dummy.

The answer points to the external-regressor arguments in R’s rugarch specification function, which supports regressors in both the conditional mean and variance equations. It also asks for the original article’s methodology and notes that a dummy variable needs a clearly defined construction. The exchange offers an implementation direction rather than a complete model specification or forecasting comparison; it gives no empirical results or guidance on selecting lags, defining the dummy, or evaluating forecast accuracy.

Key ideas

• The rugarch specification function supports external regressors in the mean and variance equations.
• The proposed analysis compares GARCH volatility forecasts with implied volatility from the VIX.
• A VIX dummy requires a defined rule for when the dummy equals one.
• The cited response does not specify a full model or report forecast results.

Tags

# Garch Model with Vix as external regressor un dummy rugarch r studio


# Garch Model with Vix as external regressor un dummy rugarch r studio












I would like to try to replicate this variance dummied model in r studio, to try to compare garch vs i.v in forecasting vol: Data : S&P 500 log-return from 03.01.2020 to 31.12.2022 Ext regressor : Vix from 03.01.2020 to 31.12.2022.

Have you some idea of how to replicate this with the rugarch package?

I tought about computing the various garch with vixt-1 as external regressor and then regress the arch vol as dipendent variable. If you have some insight let me know

## Answer by justaneconomist (score 0)

https://quant.stackexchange.com/a/77201

Can you provide the original article that you mention ? They may have explained their methodology. You can easily add external regressors in a GARCH model in R. However, you want to add a dummy variable for the VIX. How would you do it ?

Regarding the implementation, the function ugarchspec() in rugarch package allows you to add external regressors (see args(ugarchspec) ) both in the mean and the variance model ! Hope this helps you

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