This may be a naive question, but I still hope some discussion can elucidate a (so far) totally nebulous point for me.
I've recently learned that GARCH models can give one simulations of volatilities over a chosen future horizon, and understandably this has substantial applications for estimating covariance matrices and option pricing. However, can GARCH simulated volatilities be ad hoc inserted into non-GARCH econometric models, to improve them by capturing volatility clustering?
For example, if I estimate both an ARIMA(p,q,d) and GARCH(p,d) model on the same data, could they complement each other (possibly within a new model)?
If the following is generally possible, could someone with more experience describe how and why? Thank you enormously in advance.