I have 5 series of data which consist of 5-year bond yields for 5 different countries. I have estimated an EGARCH(1,1) model for each as well as the GJR-GARCH(1,1). I would like to test which of these 2 models does a better job at matching the data. I found a procedure by Engle and Ng (1993) however, it only tests a GARCH(1,1) vis-a-vis a EGARCH(1,1)However, I wondered whether there is any formal way to test whether the GJR-GARCH or the EGARCH better match the data. My series exhibit strong signs of asymmetry and as a consequence my hypothesis is that a model such as the GJR-GARCH of the EGARCH would provide a better fit to the data. However, having estimates for both of these I don't know how to choose which one is best. However, results Ljung-Box statistics are much better for the EGARCH(1,1).Thank you very much,Alan

You could pick the one with the minimum Schwartz Bayesian Criteria.