I'm trying to answer a simply posed question using a GARCH model: can we expect larger price shocks in a commodity when it's price is higher? (i.e., may we expect larger price shocks at \$100 per barrel oil versus \$20 per barrel?) My initial exploration of this question have involved using a multivariate GARCH model relating the return series and the price series, but the more I dive into the GARCH modeling method, the less I think it is appropriate. I'm essentially trying to see if the series variance is dependent on the series mean.
I already have a way of tackling this question via price regimes and change point analysis, ideally I would figure out a way to use GARCH volatility models as well. Many thanks!