I need to evaluate the goodness of fit of a few simple models for financial data. So far i have estimated the parameters for the following: GBM, Vasicek, GBM-Jump Diffusion, Heston-Nandi-GARCH and a two-state Markov chain regime switching model.
Now i want to know how well each of these models fit the data. What I have learned so far is that in order to perform the e.g. Kolmogorov test I need to apply first the probability integral transform by Diebold Gunther an Tay.
Does anyone of you know this method and can explain what exactly these guys propose for transformation? I would be grateful for any article where this transformation is explained step by step. (I've read quite a few on this but I still dont get it). Maybe anyone can provide some code?
I also pay attention to the Markov Regime Switching model such as MRS-BEKK, but I find it is really hard to estimate. Therefor it is interesting how you solve the problem.