As my master thesis aims to compare the volatility of 3 crypto-currencies, I want to find the best fitting garch model with the best fitting distribution assumption for each of my 3 crypto-currencies. But I wonder if different garch models with different distributions assumptions are comparable or if I can only compare the volatility characteristics of my crypto-currencies using each time the same type of model with the same type of distribution assumption.
For example, if the best fitting model for my first crypto-currency is a simple GARCH(1,1) with a normal distribution of the innovation process while that of the second crypto-currency is an EGARCH (1,1) with a t-distribution of the innovation process. Can I all the same compare their volatilities through their respective models?
Another question: If (according to my Information Criteria) a simple GARCH fits one of my crypto-currencies better than an EGARCH while it's the opposite for another of my crypto-currencies, can I conclude that my first crypto-currency responds less differently to negative and positive shocks than my second crypto-currency? Or should I only base such a conclusion on the parameters of EGARCH rather than on the Information Criteria?
Thanks in advance for your answers.
