Interview Question: Grand Arch Revisited

Sample Question #12 (econometrics – time series)
 
People use the GARCH model to study volatility.  Can you tell me if we can use the GARCH framework to study the correlation between two assets/time series?  If so, what additional assumptions and/or adjustments must we make to the original GARCH model?
 
(Comment: this is a very tough question. Why? First, this material is not covered in textbooks. Second, it requires a thorough understanding of the GARCH model and which assumptions can, or cannot, be "twisted" to fit the correlation scenario.)
 
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